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Higher Forms Symmetries (HFS) of a closed bosonic M2-brane theory formulated from the world-volume perspective on a compactified target space $\mathcal{M}_9 \times T^2$ are obtained. We show that the cancellation of the 't Hooft anomaly present in the theory is related to a 3-form flux with 1-gerbe structure associated to the world-volume flux quantization condition. A Wilson surface is naturally defined on the topological operator that characterize the holonomy of the M2-brane. The projection of the flux quantization condition onto the spatial part of the worldvolume, leads to a flux quantization on the M2-brane. The topological operators realise discrete symmetries associated with the winding and the flux/monopole condition. The algebra of operators is well defined., Comment: Latex, 19 pages, some references added and typos corrected

In this paper, we study the relation of the M2-brane with fluxes and monodromy in $SL(2,\mathbb{Z})$, which has a quantum discrete supersymmetric spectrum with finite multiplicity, and type IIB gauged supergravities in nine dimensions. $SL(2,\mathbb{Z})$ is the group of isotopy classes of the area preserving diffeomorphisms. The global description of these M2-branes we are considering is formulated on twisted torus bundles, and they are classified in terms of $H^2(\Sigma,\mathcal{Z}_{\mathcal{\rho}})$, or equivalently, by their coinvariants for a given monodromy subgroup. We find the 'gauge' symmetries between equivalent M2-branes, on torus bundles with monodromy, that leads to $\mathbb{R}$, $SO(2)$ or $SO(1,1)$, the symmetry groups of type IIB gauged supergravities in 9d. We obtain an explicit relation between the equivalent classes of M2-brane bundles and the mass parameters that classify the gaugings of type IIB supergravities in 9d. We also find that the symmetries, between inequivalent M2-branes on twisted torus bundles for a given monodromy, are related with $\mathbb{Z}$, $\mathcal{Z}_3$, $\mathcal{Z}_5$, $\mathcal{Z}_9$ or $\mathcal{Z}_{2n-7}$ for $n\geq 5$, the U-duality symmetry group, a subgroup of $SL(2,\mathbb{Z})$. In distinction, in the case without monodromy, related to type II maximal supergravity at low energies, its U-duality group corresponds to the full $SL(2,\mathbb{Z})$., Comment: 32 pages, 1 figure

We construct, following \cite{mpgm14,mpgm17}, a massive M2-brane (supermembrane) as the limit of a genus two M2-brane that becomes a twice punctured Riemann surface with particular boundary conditions on the fields defined on the punctures. The target space is $M_9\times LCD$, where $LCD$ is a genus one light cone diagram. It contains mass terms and a topological term associated with the non-triviality of the target surface that, at low energies, can be associated with the presence of a cosmological constant. We show that the supergravity background of the M2-brane considered in this formulation requires the presence of M9-branes acting as sources. They correspond to the 11D uplift of the characteristic D8's of Romans supergravity. To this end, we explicitly show that some of the background singularities of the massive M2-brane can be reproduced by the M9-branes found by \cite{Bergshoeff}. This establishes a relation between the Romans mass and the moduli of the massive M2-brane. When dimensionally reduced, we obtain a worldsheet Hamiltonian of a N=2 type IIA closed superstring in 10D. We denote it \textit{massive} string. The corresponding \textit{massive} string inherits a non-vanishing constant term from the topological massive M2-brane that shifts the Hamiltonian. The non-vanishing parameter is related to the non-trivial structure of the massive M2-brane background and it can be related to the Romans mass term. It also contains a modified tension due to the non-trivial dependence on the moduli and on the punctures associated with the target torus., Comment: 25 pages, 5 figures. arXiv admin note: text overlap with arXiv:2301.00686

In this paper we obtain a family of analytic solutions to the nonlinear partial differential equations that describe the dynamics of the bosonic part of the mass operator of a M2-brane compactified on $M_9\times T^2$ in the LCG with worldvolume fluxes. Those fluxes can be induced by a constant and quantized supergravity 3-form. This sector of the theory, at supersymmetric level, has the interesting property of having a discrete spectrum. We have focused on the characterization of Q-ball-like (QBL) solitons on the M2-brane with worldvolume fluxes. Two scenarios are analysed: one in which the system is isotropic and the other anisotropic. In the isotropic case, we obtain analytic families of string-like solutions to the membrane equations of motion in the presence of a non-vanishing symplectic gauge field that satisfy all constraints. We explicitly show a localised family of QBL solutions. It is demonstrated that although the solutions generally exhibit dispersion, they also allow for dispersion-free solutions. In the non-isotropic case, we obtain full-fledged membrane QBL solutions by numerical methods. We characterize some other properties of the solutions found. The dynamics of the QBL solutions are also encountered. We analyze the Lorentz boosts and Galilean transformations. Since we work in the Light Cone Gauge, the Lorentz transformed solutions are not automatically solutions, rather some extra conditions must be imposed. Only a subset of the solutions remain. We discuss some examples. The QBL solitons of the M2-brane that have been discovered contain an interaction term between the Noether charge of the Q-ball and the topological monopole charge associated with the worldvolume flux. The monopole charge increases the stability of the analytic solutions against fission..., Comment: Latex, 22 pg, 9 figures. For the sake of clarity, the writing of the paper has been improved. Three new figures and new explanations have been added and the order of sections has been changed. A new subsection on localised Q-ball-like solutions and a discussion on stability have been added. The previous results remain unchanged

In this paper, we obtain the explicit expression of the supersymmetric algebra associated with the recently proposed massive supermembrane including all surface terms. We formulate the theory as the limit of a supermembrane on a genus-two compact Riemann surface when one of the handles becomes a string attached to a torus. The formulation reduces to a supermembrane on a punctured torus with a "string spike" (in the sense of \cite{dwln}), attached to it. In this limit, we identify all surface terms of the algebra and give the explicit expression of the Hamiltonian in agreement with the previous formulation of it. The symmetry under area preserving diffeomorphisms, connected and nonconnected to the identity, is also discussed. Only parabolic $Sl(2,\mathbb{Z})$ discrete symmetries are preserved., Comment: 10 pages, 4 figures

We extend the work of Schwarz [1] to show that bound states of type IIB supersymmetric ($p, q$)-strings on a circle are associated with M2-branes irreducibly wrapped on $T^2$, or equivalently with nontrivial worldvolume fluxes. Beyond this extension we consider the Hamiltonian of an M2-brane with $C_{\pm}$ fluxes formulated on a symplectic torus bundle with monodromy. In particular, we analyze the relevant case when the monodromy is parabolic. We show that the Hamiltonian is defined in terms of the coinvariant module. We also find that the mass operator is invariant under transformations between inequivalent coinvariants. These coinvariants classify the inequivalent classes of twisted torus bundles with nontrivial monodromy for a given flux. We obtain their associated ($p,q$)-strings via double dimensional reduction, which are invariant under a parabolic subgroup of $SL(2,\mathbb{Q})$. This is the origin of the gauge symmetry of the associated gauged supergravity. These bound states could also be related to the parabolic Scherk-Schwarz reductions of type IIB string theory., Comment: 34 pages, 2 Apendices. Improvements were made in the introduction and during the manuscript

In this work we obtain classical solutions of the bosonic sector of the supermembrane theory with two-form fluxes associated to a quantized constant $C_{\pm}$ background. This theory satisfies a flux condition on the worldvolume that induces monopoles over it. Classically it is stable as it does not contain string-like spikes with zero energy in distinction with the general case. At quantum level the bosonic membrane has a purely discrete spectrum but the relevance is that the same property holds for its supersymmetric spectrum. We find for this theory spinning membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume in different approximations. By using the duality found between this theory and the so-called supermembrane with central charges, rotating membrane solutions found in that case, are also solutions of the M2-brane with $C_{\pm}$ fluxes. We generalize this result to other embeddings. We find new distinctive rotating membrane solutions, some of them including the presence of a non-vanishing symplectic gauge connection defined on its worldvolume. We obtain numerical and analytical solutions in different approximations characterizing the dynamics of the membrane with fluxes $C_{\pm}$ for different ans\"atze of the dynamical degrees of freedom. Finally we discuss the physical admissibility of some of these ans\"atze to model the components of the symplectic gauge field., Comment: Some clarifications added to section 2 and the discussion session has been enriched. Some references added. Results unchanged. Some change letter size. Latex, 33 pages, 5 figures. Accepted in JHEP

In this work we consider the existence and uniqueness of the ground state of the regularized Hamiltonian of the Supermembrane in dimensions $D= 4,\,5,\,7$ and 11, or equivalently the $SU(N)$ Matrix Model. That is, the 0+1 reduction of the 10-dimensional $SU(N)$ Super Yang-Mills Hamiltonian. This ground state problem is associated with the solutions of the inner and outer Dirichlet problems for this operator, and their subsequent smooth patching (glueing) into a single state. We have discussed properties of the inner problem in a previous work, therefore we now investigate the outer Dirichlet problem for the Hamiltonian operator. We establish existence and uniqueness on unbounded valleys defined in terms of the bosonic potential. These are precisely those regions where the bosonic part of the potential is less than a given value $V_0$, which we set to be arbitrary. The problem is well posed, since these valleys are preserved by the action of the $SU(N)$ constraint. We first show that their Lebesgue measure is finite, subject to restrictions on $D$ in terms of $N$. We then use this analysis to determine a bound on the fermionic potential which yields the coercive property of the energy form. It is from this, that we derive the existence and uniqueness of the solution. As a by-product of our argumentation, we show that the Hamiltonian, restricted to the valleys, has spectrum purely discrete with finite multiplicity. Remarkably, this is in contrast to the case of the unrestricted space, where it is well known that the spectrum comprises a continuous segment. We discuss the relation of our work with the general ground state problem and the question of confinement in models with strong interactions., Comment: Latex, 31 pages

We show the relation between three non trivial sectors of M2-brane theory formulated in the LCG connected among them by canonical transformations. These sectors correspond to the supermembrane theory formulated on a $M_9\times T^2$ on three different constant three-form backgrounds: M2-brane with constant $C_{-}$, M2-brane with constant $C_{\pm}$ and M2-brane with a generic constant $C_3$ denoted as CM2-brane. The first two exhibit a purely discrete supersymmetric spectrum once the central charge condition, or equivalently, the corresponding flux condition has been turned on. The CM2-brane is conjectured to share this spectral property once that fluxes $C_{\pm}$ are turned on. As shown in [1] they are duals to three inequivalent sectors of the D2-branes with specific worldvolume and background RR and NSNS quantization conditions on each case., Comment: 6 pages. To be considered for publication in the Proc. of the XXII Chilean Physics Symposium 2020, Journal of Physics Conference Series IOP

We present the formulation of the bosonic Hamiltonian M2-brane compactified on a twice punctured torus following the procedure proposed in \cite{mpgm14}. In this work we analyse two possible metric choice, different from the one used in \cite{mpgm14}, over the target space and study some of the properties of the corresponding Hamiltonian., Comment: Proceeding SOCHIFI 2020 (Sociedad Chilena de F\'isica). 6 pages

We obtain the Hamiltonian formulation of the 11D Supermembrane theory non-trivially compactified on a twice-punctured torus times a 9D Minkowski space-time. It corresponds to a M2-brane formulated in 11D space with ten non-compact dimensions. The critical points like the poles and the zeros of the fields describing the embedding of the Supermembrane in the target space are treated rigorously. The non-trivial compactification generates non-trivial mass terms appearing in the bosonic potential, which dominate the full supersymmetric potential and should render the spectrum of the (regularized) Supermembrane discrete with finite multiplicity. The behaviour of the fields around the punctures generates a cosmological term in the Hamiltonian of the theory. The massive supermembrane can also be seen as a nontrivial uplift of a supermembrane torus bundle with parabolic monodromy in $M_9\times T^2$. The moduli of the theory is the one associated with the punctured torus, hence it keeps all the nontriviality of the torus moduli even after the decompactification process to ten noncompact dimensions. The formulation of the theory on a punctured torus bundle is characterized by the $(1,1)-Knots$ associated with the monodromies., Comment: 25 pages, 5 figures

In this work we obtain dynamical solutions of the bosonic sector of the supermembrane theory with central charges formulated on $M_9\times T^2$, denoted by MIM2. The theory with this condition corresponds to a supermembrane with a $C_-$ flux. This sector of the M2-brane is very interesting since classically is stable as it does not contain string-like spikes with zero energy and at quantum level has a purely discrete supersymmetric spectrum. We find rotating solutions of the MIM2 equations of motion fulfilling all of the constraints. By showing that the MIM2 mass operator, contains the mass operator discussed in [Brugues, Rojo, Russo, Nucl. Phys. B 710, 2005], then we show that the rotating solutions previously found in the aforementioned work that also satisfy the topological central charge condition, are solutions of the MIM2. Finally, we find new distinctive rotating membrane solutions that include the presence of a new non-vanishing dynamical scalar field defined on its worldvolume., Comment: 6 pages, 1 figure. Section 4 re-worked, conclusions modified. Submitted to Journal of Physics: Conference Series Proceedings Chilean Physics Symposium 2020 (SOCHIFI 2020)

We obtain the bosonic D-brane description of toroidally compactified non-trivial M2-branes with the unique property of having a purely discrete supersymmetric regularized spectrum with finite multiplicity. As a byproduct, we generalize the previous Hamiltonian formulation to describe a M2-brane on a completely general constant quantized background $C_3$ denoted by us as CM2-brane. We show that under this condition, the theory is equivalent to a more restricted one, denoted as an M2-brane with $C_\pm$ fluxes, which has been shown to have good quantum behavior. As a result, the spectral properties of both sectors must be the same.We then obtain its bosonic D-brane description and discover new symmetries. We find that it contains a new symplectic gauge field in addition to the expected U(1) Dirac-Born-Infeld gauge symmetry and a nontrivial $U(1)$ associated with the presence of 2-form fluxes. Its bundle description takes on a new structure in the form of a twisted torus bundle. By turning off some of the fields, the D-brane description of other toroidally nontrivial M2-brane sectors can be obtained from this one. The possibility of reinterpreting these sectors in terms of Dp-brane bound states is discussed. These D-brane descriptions constitute String theory sectors with a quantum consistent uplift to M-theory., Comment: 34 pages. Some typos were improved and the title was changed

We show that the $D=11$ Supermembrane theory (M2-brane) compactified on a $M_9 \times T^2$ target space, with constant fluxes $C_{\pm}$ naturally incorporates the geometrical structure of a twisted torus. We extend the M2-brane theory to a formulation on a twisted torus bundle. It is consistently fibered over the world volume of the M2-brane. It can also be interpreted as a torus bundle with a nontrivial $U(1)$ connection associated to the fluxes. The structure group $G$ is the area preserving diffeomorphisms. The torus bundle is defined in terms of the monodromy associated to the isotopy classes of symplectomorphisms with $\pi_{0} (G) = SL(2,Z)$, and classified by the coinvariants of the subgroups of $SL(2,Z)$. The spectrum of the theory is purely discrete since the constant flux induces a central charge on the supersymmetric algebra and a modification on the Hamiltonian which renders the spectrum discrete with finite multiplicity. The theory is invariant under symplectomorphisms connected and non connected to the identity, a result relevant to guaranteed the U-dual invariance of the theory. The Hamiltonian of the theory exhibits interesting new $U(1)$ gauge and global symmetries on the worldvolume induced by the symplectomorphim transformations. We construct explicitly the supersymmetric algebra with nontrivial central charges. We show that the zero modes decouple from the nonzero ones. The nonzero mode algebra corresponds to a massive superalgebra that preserves either $1/2$ or $1/4$ of the original supersymmetry depending on the state considered., Comment: Latex, 27pg

The formulation of supermembrane theory on nontrivial backgrounds is discussed. In particular, we obtain the Hamiltonian of the supermembrane on a background with constant bosonic three form on a target space $M_9 \times T^2$., Comment: Proceeding SOCHIFI 2018 (Sociedad Chilena de F\'isica). 6 pages

We describe a compactified Supermembrane, or M2-brane, with 2-form fluxes generated by constant three-forms that are turned on a 2-torus of the target space $M_9\times T^2$. We compare this theory with the one describing a $11D$ M2-brane formulated on $M_9\times T^2$ target space subject to an irreducible wrapping condition. We show that the flux generated by the bosonic 3-form under consideration is in a one to one correspondence to the irreducible wrapping condition. After a canonical transformation both Hamiltonians are exactly the same up to a constant shift in one particular case. Consequently both of them, share the same spectral properties. We conclude that the Hamiltonian of the M2-brane with 2-form target space fluxes on a torus has a purely discrete spectrum with eigenvalues of finite multiplicity and it can be considered to describe a new sector of the microscopic degrees of freedom of M-theory. We also show that the total membrane momentum in the direction associated to the flux condition acquires a quantized contribution in correspondence to the flux units that have been turned on., Comment: Latex, 15 pages, title changed, paper revised, results improved

We analyse the measure of the regularized matrix model of the supersymmetric potential valleys, $\Omega$, of the Hamiltonian of non zero modes of supermembrane theory. This is the same as the Hamiltonian of the BFSS matrix model. We find sufficient conditions for this measure to be finite, in terms the spacetime dimension. For $SU(2)$ we show that the measure of $\Omega$ is finite for the regularized supermembrane matrix model when the transverse dimensions in the light cone gauge $\mathrm{D}\geq 5$. This covers the important case of seven and eleven dimensional supermembrane theories, and implies the compact embedding of the Sobolev space $H^{1,2}(\Omega)$ onto $L^2(\Omega)$. The latter is a main step towards the confirmation of the existence and uniqueness of ground state solutions of the outer Dirichlet problem for the Hamiltonian of the $SU(N)$ regularized $\mathrm{D}=11$ supermembrane, and might eventually allow patching with the inner solutions., Comment: Latex, 11 pages, reference added

Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterised either as an F-term or Fayet-Iliopoulos D-term. Using again the modular symmetry, we show that 4D non-linear supergravities that descend from string theory have an enhanced protection from quantum corrections by non-renormalisation theorems. The superpotential giving rise to metastable de Sitter vacua is robust against perturbative string-loop and $\alpha'$ corrections., Comment: 33 pages

Supermembrane compactified on a $M_9\times T^2$ target space is globally described by the inequivalent classes of torus bundles over torus. These torus bundles have monodromy in $SL(2,Z)$ when they correspond to the nontrivial central charge sector and they are trivial otherwise. The first ones contain eight inequivalent classes of M2-brane bundles which at low energies, are in correspondence with the eight type II gauged supergravities in $9D$. The relation among them is completely determined by the global action of T-duality which interchanges topological invariants of the two tori. The M2-brane torus bundles are invariant under $SL(2,Z)\times SL(2,Z) \times Z_2$. From the effective point of view, there is another dual invariant theory, called Double Field Theory which describe invariant actions under $O(D,D)$. Globally it is formulated in terms of doubled $2D$ torus fibrations over the spacetime with a monodromy given by $O(D,D,Z)$. In this note we discuss T-duality global aspects considered in both theories and we emphasize certain similarities between both approaches which could give some hints towards a deeper relationship between them., Comment: 10 pages. arXiv admin note: text overlap with arXiv:1604.02579

In this paper we obtain the complete classification of the inequivalent classes of M2-brane symplectic torus bundles with monodromy in $SL(2,Z)$ and their precise U-duality relations among them. There are eight inequivalent classes of bundles whose monodromy groups, at low energies, are in correspondence with the gauging groups of the eight type II gauged supergravities in nine dimensions. Four of those have been previously found and they correspond to the 'type IIB side'. In this paper we provide the explicit realization of the remaining four classes associated to the 'type IIA side'. The precise M2-brane U-duality relations between the eight inequivalent classes of bundles have allowed to identified the remaining four ones. We conjecture that the classes of gaugings -- classifying the eight types of II gauged supergravity in nine dimensions -- are determined by the inequivalent coinvariant classes associated to the base and the fiber of the supermembrane bundles and their duals., Comment: Latex 13 pages, 1 figures. The paper has been re-written for sake of clarity and rewritten in order to answer observations made by the referee. Results are totally unchanged. Version accepted for publication at PRD

We remark that the two 10D massive deformations of the $N=2$ maximal type IIA supergravity (Romans and HLW supergravity) are associated to the low energy limit of the uplift to 10D of M2-brane torus bundles with parabolic monodromy linearly and non-linearly realized respectively. Romans supergravity corresponds to M2-brane compactified on a twice-punctured torus bundle., Comment: latex, 4pg, Contribution to the proceedings of "The String Theory Universe" workshop in Leuven, 7-11 Sept 2015

We investigate a string-inspired axion extension of the standard model obtained from Type II superstrings using quiver method. In the first part, we discuss intersecting Type IIA D6-branes wrapping non trivial 3-cycles in the presence of the Peccei-Quinn symmetry U(1)$_{PQ}$. Concretely, a complex scalar field $\phi =\rho exp(\frac{i\sigma}{f_{\sigma}})$, where $\sigma$ is a closed string axion generates a general fermion Yukawa coupling weighted by a flavor-dependent power $n_{f}$ taking specific values. Using string theory and standard model data, we find that the corresponding axion window is in the allowed range $10^{9}GeV\leq f_{\sigma}\leq 10^{12}GeV $ matching with the recent cosmological results. Then, we extend these results to the case of the hyperbolic quiver whose the moduli is related to the stringy axion using root systems of ADE Lie algebras. For the hyperbolic quiver case, we observe that the closed axion decay constant becomes disentangled from the string scale., Comment: 19 pages, Latex, typos corrected, some reference added

In this note we explicitly show how the generalization of the T-duality symmetry of the supermembrane theory compactified in M9xT2 can be reduced to a parabolic subgroup of SL(2,Z) that acts non-linearly on the moduli parameters and on the KK and winding charges of the supermembrane. This is a first step towards a deeper understanding of the dual relation between the parabolic type II gauged supergravity in nine dimensions., Comment: 6 pages, Latex, Proceedings for the XIX Simposio Chileno de Fisica, SOCHIFI 2014 Conference, 26-28 November 2014, held at Concepcion U., Chile

We establish a general framework for the analysis of boundary value problems of matrix models at zero energy on compact regions. We derive existence and uniqueness of ground state wavefunctions for the mass operator of the $D=11$ regularized supermembrane theory, that is the $\mathcal{N}=16$ supersymmetric $SU(N)$ matrix model, on balls of finite radius. Our results rely on the structure of the associated Dirichlet form and a factorization in terms of the supersymmetric charges. They also rely on the polynomial structure of the potential and various other supersymmetric properties of the system., Comment: Latex, 26 pages. We have added some comments at the introduction in order to make it easier for the reader. Results of the paper unchanged

We discuss the existence and uniqueness of wavefunctions for inhomogenoeus boundary value problems associated to x^2y^2-type matrix model on a bounded domain of R^2. Both properties involve a combination of the Cauchy-Kovalewski Theorem and a explicit calculations., Comment: 3 pages, Latex Proceedings for the XIX Simposio Chileno de Fisica, SOCHIFI 2014 Conference, 26-28 November 2014, held at Concepcion U., Chile

We show the existence and uniqueness of a massless supersymmetric ground state wavefunction of a SU(2) matrix model in a bounded smooth domain with Dirichlet boundary conditions. This is a gauge system and we provide a new framework to analyze the quantum spectral properties of this class of supersymmetric matrix models subject to constraints which can be generalized for arbitrary number of colors., Comment: 12 pages, Latex. Somme clarifications. Minor changes. Version to appear at NPB

In this work we examine the existence and uniqueness of the groundstate of a SU(N)x G2 octonionic matrix model on a bounded domain of R^N. The existence and uniqueness argument of the groundstate wavefunction follows from the Lax-Milgram theorem. Uniqueness is shown by means of an explicit argument which is drafted in some detail., Comment: Latex, 6 pages

Recently, a new gauging procedure called Sculpting mechanism was proposed to obtain the M-theory origin of type II gauged Supergravity theories in 9D. We study this procedurein detail and give a better understanding of the different deformations and changes in fiber bundles, that are able to generate new relevant physical gauge symmetries in the theory. We discuss the geometry involved in the standard approach (Noether-like) and in the new Scultping-like one and comment on possible new applications., Comment: 9 pages, latex, Notation and typos reviewed, more clear explanations, results unchanged

In this note I review the role played by dualities in the Supermembrane Theory compactified on a torus. Supermembrane theory realize S, T, so U-duality, as exact symmetries of the theory. There are two well defined sectors: with and without central charges. Both sectors have the SL(2,Z)xZ2 U-duality group in 9D as a symmetry of the theory, but the supermembrane with central charges, also exhibits an extra SL(2,Z) symmetry of the theory associated to the diffeomorphisms not connected with the identity changing the homology basis. The Z2 symmetry is T-duality transformation that acts on the supermembrane and generalize that of the string. This T-duality transformation acts locally and also globally on the supermembrane theory. It has a natural description in terms of the cohomology of the base manifold and the homology of the target torus. When only string-like states are preserved, one recovers both type II string theories in 9D. If one also consider properly limit of the T-duality transformation characterizing the supermembrane, the usual closed string T-duality transformation between the type IIA and type IIB mass operators is recovered., Comment: 17 pg, latex. arXiv admin note: substantial text overlap with arXiv:1203.2767

We show that the supermembrane theory compactified on a torus is invariant under T-duality. There are two different topological sectors of the compactified supermembrane (M2) classified according to a vanishing or nonvanishing second cohomology class. We find the explicit T-duality transformation that acts locally on the supermembrane theory and we show that it is an exact symmetry of the theory. We give a global interpretation of the T-duality in terms of bundles. It has a natural description in terms of the cohomology of the base manifold and the homology of the target torus. We show that in the limit when the torus degenerate into a circle and the M2 mass operator restricts to the string-like configurations, the usual closed string T-duality transformation between the type IIA and type IIB mass operators is recovered. Moreover if we just restrict M2 mass operator to string-like configurations but we perform a generalized T-duality we find the SL(2,Z) non-perturbative multiplet of IIA., Comment: 8pages, Latex. Proceeding of the XXI International Workshop on Geometry and Physics held at U.Burgos, Spain

The M-theory origin of the IIB gauged supergravities in nine dimensions, classified according to the inequivalent classes of monodromy, is shown to exactly corresponds to the global description of the supermembrane with central charges. The global description is a realization of the sculpting mechanism of gauging (arXiv:1107.3255) and it is associated to particular deformation of fibrations. The supermembrane with central charges may be formulated in terms of sections on symplectic torus bundles with SL(2,Z) monodromy. This global formulation corresponds to the gauging of the abelian subgroups of SL(2,Z) associated to monodromies acting on the target torus. We show the existence of the trombone symmetry in the supermembrane formulated as a non-linear realization of the SL(2,Z) symmetry and construct its gauging in terms of the supermembrane formulated on an inequivalent class of symplectic torus fibration. The supermembrane also exhibits invariance under T-duality and we find the explicit T-duality transformation. It has a natural interpretation in terms of the cohomology of the base manifold and the homology of the target torus. We conjecture that this construction also holds for the IIA origin of gauged supergravities in 9D such that the supermembrane becomes the origin of all type II supergravities in 9D. The geometric structure of the symplectic torus bundle goes beyond the classification on conjugated classes of SL(2,Z). It depends on the elements of the coinvariant group associated to the monodromy group. The possible values of the (p,q) charges on a given symplectic torus bundle are restricted to the corresponding equivalence class defining the element of the coinvariant group., Comment: 41 pages, Latex. Typos corrected, references added, appendix added. Sections enlarged with more examples and clarifying explanations. Minor corrections in section 8. Results unchanged

We provide a mechanism of gauging a theory based on a particular way to embed a theory on a target space such that a nontrivial fibration is produced. A connection over a nontrivial fibration with monodromy provides a natural framework for a new way of gauging a theory. Moreover, properties of the global symmetry of the original theory are included in a particular way in the new theory. This mechanism for gauging a symmetry preserves the total number of degrees of freedom in distinction with the classical one. We consider a particular example to illustrate the mechanism: by reinterpreting the supermembrane with central charges as a gauged supermembrane of the compactified supermembrane according to this new sense of gauging. Further applications are also discussed., Comment: Latex, 27 pages

We discuss a class of 3-dimensional N=4 Chern-Simons (CS) quiver gauge models obtained from M-theory compactifications on singular complex 4-dimensional hyper-Kahler (HK) manifolds, which are realized explicitly as a cotangent bundle over two-Fano toric varieties V^2. The corresponding CS gauge models are encoded in quivers similar to toric diagrams of V^2. Using toric geometry, it is shown that the constraints on CS levels can be related to toric equations determining V^2., Comment: 14pg, 1 Figure, latex

In this note we summarize some of the properties found in several papers. We characterize spectral properties of the quantum mechanical hamiltonian of theories with fermionic degrees of freedom beyond semiclassical approximation. We obtain a general class of bosonic polynomial potentials for which the Schr\"oedinger operator has a discrete spectrum. This class includes all the scalar potentials in membrane, 5-brane, p-branes, multiple M2 branes, BLG and ABJM theories. We also give a sufficient condition for discreteness of the spectrum for supersymmmetric and non supersymmetric theories with a fermionic contribution. We characterize then the spectral properties of different theories: the BMN matrix model, the supermembrane with central charges and a bound state of $N$ D2 with $m$ D0. We show that, while the first two models have a purely discrete spectrum with finite multiplicity, the latter has a continuous spectrum starting from a constant given in terms of the monopole charge., Comment: 10pg, Latex, Contributions to the Conference XVI European Workshop on String Theory 2010, Madrid June 14-18, 2010

We give the explicit formulation of the 11D supermembrane as a symplectic torus bundle with non trivial monodromy and non vanishing Euler class. This construction allows a classification of all supermembranes showing explicitly the discrete SL(2,Z) symmetries associated to dualities. It hints as the origin in M-theory of the gauging of the effective theories associated to string theories., Comment: 13 pages, Latex

We formulate a general sufficiency criterion for discreteness of the spectrum of both supersymmmetric and non-su-persymmetric theories with a fermionic contribution. This criterion allows an analysis of Hamiltonians in complete form rather than just their semiclassical limits. In such a framework we examine spectral properties of various (1+0) matrix models. We consider the BMN model of M-theory compactified on a maximally supersymmetric pp-wave background, different regularizations of the supermembrane with central charges and a non-supersymmetric model comprising a bound state of N D2 with m D0. While the first two examples have a purely discrete spectrum, the latter has a continuous spectrum with a lower end given in terms of the monopole charge., Comment: 40 pages, 5 figures

We obtain a general class of polynomials for which the Schrodinger operator has a discrete spectrum. This class includes all the scalar potentials in membrane, 5-brane, p-branes, multiple M2 branes, BLG and ABJM theories. We provide a proof of the discreteness of the spectrum of the associated Schrodinger operators. This a a first step in order to analyze BLG and ABJM supersymmetric theories from a non-perturbative point of view., Comment: 17pg, Latex. Some more explanatory comments and references added.

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M9xT2 (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for any number of M2-branes., Comment: Contribution to the Proceedings of the Dubna International SQS'09 Workshop ("Supersymmetries and Quantum Symmetries-2009", July 29 - August 3, 2009. 12pg, Latex

We obtain a U(M) action for supermembranes with central charges in the Light Cone Gauge (LCG). The theory realizes all of the symmetries and constraints of the supermembrane together with the invariance under a U(M) gauge group with M arbitrary. The worldvolume action has (LCG) N=8 supersymmetry and it corresponds to M parallel supermembranes minimally immersed on the target M9xT2 (MIM2). In order to ensure the invariance under the symmetries and to close the corresponding algebra, a star-product determined by the central charge condition is introduced. It is constructed with a nonconstant symplectic two-form where curvature terms are also present. The theory is in the strongly coupled gauge-gravity regime. At low energies, the theory enters in a decoupling limit and it is described by an ordinary N=8 SYM in the IR phase for any number of M2-branes. We analyze also other limits of the theory: when M goes to we obtain a condensate of M2-branes. If we consider, instead of the exact action, its matrix regularized version, for suitable large N but with a finite number of colors, the algebra of the first class-constraints also closes with the ordinary product and we obtain a regularized 2+1D SU(M) SYM theory in the IR phase that is coupled to the SU(N) regularized supermembrane action. The supersymmetric regularized theory with the ordinary product has purely discrete spectrum. Our theory with the star-product is a full-fledged description of multiple M2-branes minimally immersed in distinction with other constructions that represent multiple M2-branes in the low energy approximation., Comment: 30pg, Latex, Typos corrected, references added, some more explanatory comments

In this note we summarize some of the quantum properties found since the early 80's until nowdays that characterize at quantum level the spectrum of the supermembrane. In particular we will focus on a topological sector of the 11D supermembrane that, contrary to the general case, has a purely discrete spectrum at supersymmetric level. This construction has been consistently implemented in different types of backgrounds: toroidal and orbifold-type with G2 structure able to lead to a true G2 compactification manifold. This theory has N=1 supersymmetries in 4D. comment on the relevant points of this construction as well as on its spectral characteristics. We will also make some comments on the quantum properties of some effective formulation of multiple M2's theories recently found., Comment: 7pg, latex. Contribution to the RTN proceedings Varna 08

In this note we summarize some of the properties found in [1], and its relation with [2]. We comment on the construction of the action of the 11D supermembrane with nontrivial central charges minimally immersed on a 7D toroidal manifold is obtained (MIM2).The transverse coordinates to the supermembrane are maps to a 4D Minkowski space-time. The action is invariant under additional symmetries in comparison to the supermembrane on a 11D Minkowski target space. The hamiltonian in the LCG is invariant under conformal transformations on the Riemann surface base manifold. The spectrum of the regularized hamiltonian is discrete with finite multiplicity. Its resolvent is compact. Susy is spontaneously broken, due to the topological central charge condition, to four supersymmetries in 4D, the vacuum belongs to an N=1 supermultiplet. When assuming the target-space to be an isotropic 7-tori, the potential does not contain any flat direction, it is stable on the moduli space of parameters. Moreover due to the discrete symmetries of the hamiltonian, there are only 7 possible minimal holomorphic immersions of the MIM2 on the 7-torus. When these symmetries are identified on the target space, it corresponds to compactify the MIM2 on a orbifold with G2 structure. Once the singularities are resolved it leads to the compactification of the MIM2 on a G2 manifold as shown in [2]., Comment: 6pg.latex, w-art.class. To appear in the proceedings "RTN ForcesUniverse" Valencia, 1-5 October, Spain, 2007

We construct the 11D supermembrane with topological central charges induced through an irreducible winding on a G2 manifold realized from the T7/Z2xZ2xZ2 orbifold construction. The hamiltonian H of the theory on a T7 target has a discrete spectrum. Within the discrete symmetries of H associated to large diffeomorphisms, the Z2xZ2xZ2 group of automorphisms of the quaternionic subspaces preserving the octonionic structure is relevant. By performing the corresponding identification on the target space, the supermembrane may be formulated on a G2 manifold, preserving the discretness of its supersymmetric spectrum. The corresponding 4D low energy effective field theory has N=1 supersymmetry., Comment: Reviewed version. spectral propertis discussed, two more sections added, 27 pages,Latex

The SL(2,Z) duality symmetry of IIB superstring is naturally realized on the D=11 supermembrane restricted to have central charges arising from a nontrivial wrapping. This supermembrane is minimally immersed on the target space (MIM2). The hamiltonian of the MIM2 has a discrete quantum spectrum. It is manifestly invariant under the SL(2,Z) symmetry associated to the conformal symmetry on the base manifold and under a SL(2,Z) symmetry on the moduli of the target space. The mass contribution of the string states on the MIM2 is obtained by freezing the remaining degrees of freedom. It exactly agrees with the perturbative spectrum of the (p,q) IIB and IIA superstring compactified on a circle. We also construct a MIM2 in terms of a dual target space, then a (p,q) set of non-perturbative states associated to the IIA superstring is obtained., Comment: 32pages, latex

The action of the 11D supermembrane with nontrivial central charges compactified on a 7D toroidal manifold is obtained. It describes a supermembrane evolving in a 4d Minkowski space-time. The action is invariant under additional symmetries in comparison to the supermembrane on a Minkowski target space. The hamiltonian in the LCG is invariant under conformal transformations on the Riemann surface base manifold. The spectrum of the regularized hamiltonian is discrete with finite multiplicity. Its resolvent is compact. Susy is spontaneously broken, due to the topological central charge condition, to four supersymmetries in 4D, the vacuum belongs to an N=1 supermultiplet. When assuming the target-space to be an isotropic 7-tori, the potential does not contain any flat direction, it is stable on the moduli space of parameters., Comment: Latex, 19pg

Anomalous U(1)'s are ubiquitous in 4D chiral string models. Their presence crucially affects the process of moduli stabilisation and cannot be neglected in realistic set-ups. Their net effect in the 4D effective action is to induce a matter field dependence in the non-perturbative superpotential and a Fayet-Iliopoulos D-term. We study flux compactifications of IIB string theory in the presence of magnetised D7 branes. These give rise to anomalous U(1)'s that modify the standard moduli stabilisation procedure. We consider simple orientifold models to determine the matter field spectrum and the form of the effective field theory. We apply our results to one-modulus KKLT and multi-moduli large volume scenarios, in particular to the Calabi-Yau P^4_{[1,1,1,6,9]}. After stabilising the matter fields, the effective action for the Kahler moduli can acquire an extra positive term that can be used for de Sitter lifting with non-vanishing F- and D-terms. This provides an explicit realization of the D-term lifting proposal of hep-th/0309187., Comment: 35 pages, 1 figure. v2: Minor changes, references added

In this note we summarize some of the results found recently in hep-th/0609054. We show the pure discretness of the non-perturbative quantum spectrum of a symplectic Yang-Mills theory defined on a Riemann surface of positive genus, living in a target space that, in particular, can be 4D. This theory corresponds to the membrane with central charges. The presence of the central charge induces a confinement in the phase at zero temperature. When the energy rises, the center of the group breaks and the theory enters in a quark-plasma phase after a topological transition, corresponding to the N=4 wrapped supermembrane., Comment: 5pg, latex, w-art class. To appear in the proceedings "RTN ForcesUniverse" Naples, October 9-13, 2006

The spectrum of the bosonic sector of the D=11 supermembrane with central charges is shown to be discrete and with finite multiplicities, hence containing a mass gap. The result extends to the exact theory our previous proof of the similar property for the SU(N) regularised model and strongly suggest discreteness of the spectrum for the complete Hamiltonian of the supermembrane with central charges. This theory is a quantum equivalent to a symplectic non-commutative super-Yang-Mills in 2+1 dimensions, where the space-like sector is a Riemann surface of positive genus. In this context, it is argued how the theory in 4D exhibits confinement in the N=1 supermembrane with central charges phase and how the theory enters in the quark-gluon plasma phase through the spontaneous breaking of the centre. This phase is interpreted in terms of the compactified supermembrane without central charges., Comment: 33 pages, Latex. In this new version, several changes have been made and various typos were corrected

We obtain the precise condition on the potentials of Yang-Mills theories in 0+1 dimensions and D0 brane quantum mechanics ensuring the discretness of the spectrum. It is given in terms of a moment of inertia of the membrane. From it we obtain a bound for the mass gap of any D+1 Yang-Mills theory in the slow-mode regime. In particular we analyze the physical case D=3. The quantum mechanical behavior of the theories, concerning its spectrum, is determined by harmonic oscillators with frequencies given by the inertial tensor of the membrane. We find a class of quantum mechanic potential polynomials of any degree, with classical instabilities that at quantum level have purely discrete spectrum., Comment: 12pages, Latex, minor changes, more explanatory comments

We study the scalar potential in supersymmetric (orientifolded) Calabi Yau compactifications of Type IIB theory. We present a new mechanism to stabilize all closed string moduli at leading order in \alpha^{'} by introducing consistently fluxes. As usual we consider the dilaton and the complex structure moduli stabilized by turning on three-form fluxes that couple to the F-part of the scalar potential. Kahler moduli get fixed by the combined action of the flux-induced scalar masses with magnetic fields of the open string sector, and Fayet-Illiopoulos terms. For supersymmetric three-form fluxes the model is N=1, otherwise the mass terms are the scalar soft breaking terms of the SM fields. For the case of imaginary self dual three-form fluxes (ISD), the mass terms are positive and the minimum at the potential is at exactly zero energy. We argue that, under generic assumptions, this is a general mechanism for the full stabilization of closed string moduli. The vacua depend explicitly on the fluxes introduced in the manifold. A concrete realization of this mechanism on type IIB on a (T^ {6}/Z_{2}xZ_{2}) orientifold is provided., Comment: 26 pages, Latex. Typos corrected and some references added

We discuss the consistency of the D=11 supermembranes with non zero central charge arising from a nontrivial winding CSNW. The spectrum of its regularized Hamiltonian is discrete and its heat kernel in terms of a Feynman formula may be rigorously constructed. The $N\to\infty$ limit is discussed. Since CSNW is equivalent to a noncommutative supersymmetric gauge theory on a general Riemann surface, its consistency provides a proof that all of them are well defined quantum theories. We interpret the supermembrane with central charge $n$, in the type IIA picture, as a bundle of D2 branes with $n$ units of D0 charge induced by a nonconstant magnetic flux., Comment: 7 pages, 1 figure