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Abstract We explore the properties of Ω-deformed M-theory, with particular focus on the ℂ ϵ 1 $$ {\mathbb{C}}_{\epsilon_1} $$ × ℂ ϵ 2 $$ {\mathbb{C}}_{\epsilon_2} $$ × ℂ ϵ 3 $$ {\mathbb{C}}_{\epsilon_3} $$ background and coupling to Ω-deformed M2 and M5 brane world-volume theories.

Abstract In this work, we study the local zeta functions of Calabi-Yau fourfolds. This is done by developing arithmetic deformation techniques to compute the factor of the zeta function that is attributed to the horizontal four-form cohomology. This, in turn, is sensitive to the complex structure of the fourfold. Focusing mainly on examples of fourfolds with a single complex structure parameter, it is demonstrated that the proposed arithmetic techniques are both applicable and consistent. We present a Calabi-Yau fourfold for which a factor of the horizontal four-form cohomology further splits into two pieces of Hodge type (4, 0) + (2, 2) + (0, 4) and (3, 1) + (1, 3). The latter factor corresponds to a weight-3 modular form, which allows expressing the value of the periods in terms of critical values of the L-function of this modular form, in accordance with Deligne’s conjecture. The arithmetic considerations are related to M-theory Calabi-Yau fourfold compactifications with background four-form fluxes. We classify such background fluxes according to their Hodge type. For those fluxes associated to modular forms, we express their couplings in the low-energy effective action in terms of L-function values.

Abstract It has been recently suggested that the strong Emergence Proposal is realized in M-theory limits by integrating out all light towers of states with a typical mass scale not larger than the species scale, i.e. the eleventh dimensional Planck mass. Within the BPS sector, these are transverse M2- and M5-branes, that can be wrapped and particle-like, carrying Kaluza-Klein momentum along the compact directions. We provide additional evidence for this picture by revisiting and investigating further the computation of R 4-interactions in M-theory à la Green-Gutperle-Vanhove. A central aspect is a novel UV-regularization of Schwinger-like integrals, whose actual meaning and power we clarify by first applying it to string perturbation theory. We consider then toroidal compactifications of M-theory and provide evidence that integrating out all light towers of states via Schwinger-like integrals thus regularized yields the complete result for R 4-interactions. In particular, this includes terms that are tree-level, one-loop and space-time instanton corrections from the weakly coupled point of view. Finally, we comment on the conceptual difference of our approach to earlier closely related work by Kiritsis-Pioline and Obers-Pioline, leading to a correspondence between two types of constrained Eisenstein series.

Abstract We analyze correlation functions of SU(k) × SU(2) F flavor currents in a family of three-dimensional N $$ \mathcal{N} $$ = 4 superconformal field theories, combining analytic bootstrap methods with input from supersymmetric localization. Via holographic duality, we extract gluon and graviton scattering amplitudes of M-theory on AdS4 × S 7/ℤ k which contains a ℂ2/ℤ k orbifold singularity. From these results, we derive aspects of the effective description of M-theory on the orbifold singularity beyond its leading low energy limit. We also determine a threshold correction to the holographic correlator from the combined contribution of two-loop gluon and tree-level bulk graviton exchange.

Abstract We study 3D N $$ \mathcal{N} $$ = 2 supersymmetric field theories geometrically engineered from M-theory on non-compact Calabi-Yau fourfolds (CY4). We establish a detailed dictionary between the geometry and topology of non-compact CY4 and the physics of 3D N $$ \mathcal{N} $$ = 2 theories in three different regimes. The first one is the Coulomb branch description when the CY4 is smooth. The second one is non-abelian gauge theory when the CY4 has a degenerate ℙ1-fibration structure. The third one is the strongly coupled SCFT from a CY4 singularity. We find interesting flavor symmetry enhancements in the singular limit of CY4, as well as an interesting and previously unexplored phenomenon in 3D, termed “flavor symmetry duality”. Many examples are analyzed with an emphasis on toric CY4s and ℂ4 orbifolds with crepant resolutions. We develop a new brane box method to study the physics of Coulomb branch of 3D N $$ \mathcal{N} $$ = 2 theory that admits a toric construction. Via IIB/M-theory duality we find that the brane box diagram living in ℝ3 can be physically realized as a configuration of intersecting 4-branes which are extended objects in 8D maximal supersymmetric theory, which is shown to be consistent via various chains of dualities. The rank, effective gauge coupling and certain hints to flavor symmetry enhancement of the 3D N $$ \mathcal{N} $$ = 2 theory are read off from the brane box and cross-checked against the results obtained from geometric engineering. The exotic branes in 8D maximal supersymmetric theory and the 4-string junctions thereof are shown to play a crucial role in the construction of the brane box.

Abstract It has recently been realised that there are supersymmetry-preserving non-relativistic decoupling limits associated with each half-BPS object in String Theory and M-Theory. We argue that, given a p-brane and a q-brane for which there is a quarter-BPS intersecting configuration, the p-brane decoupling limit of the q-brane’s worldvolume QFT is necessarily equal to the reciprocal q-brane decoupling limit of the p-brane’s worldvolume theory. This is explicitly shown for the cases of the D0-D4 and D1-D3 systems. As an application of this idea, we use the reciprocal pair of limits in the M2-M5 system to describe the dynamics of interacting self-dual strings in the six-dimensional N $$ \mathcal{N} $$ = (2, 0) theory. We also discuss the limits of the dual gravitational theories and, using symmetries, argue that the duality is maintained by the limits.

Abstract The squashed seven-sphere operator spectrum is completed by deriving the spectrum of the spin-3/2 operator. The implications of the results for the AdS 4 N $$ \mathcal{N} $$ = 1 supermultiplets obtained from compactification of eleven-dimensional supergravity are analysed. The weak G 2 holonomy plays an important role when solving the eigenvalue equations on the squashed sphere. Here, a novel and more universal algebraic approach to the whole eigenvalue problem on coset manifolds is provided. Having obtained full control of all the operator spectra, we can finally determine the irreps D(E 0 , s) for all supermultiplets in the left-squashed vacuum. This includes an analysis of possible boundary conditions. By performing an orientation flip on the seven-sphere, we also obtain the full spectrum for the non-supersymmetric right-squashed compactification which is of interest in the swampland context and in particular for the AdS swampland conjecture. Here, a number of boundary condition ambiguities arise making the analysis of dual marginal operators somewhat involved. This work is a direct continuation of [1] and [2].

Abstract We study a decoupling limit of M-theory where the three-form gauge potential becomes critical. This limit leads to nonrelativistic M-theory coupled to a non-Lorentzian spacetime geometry. Nonrelativistic M-theory is U-dual to M-theory in the discrete light cone quantization, a non-perturbative approach related to the Matrix theory description of M-theory. We focus on the compactification of nonrelativistic M-theory over a two-torus that exhibits anisotropic behaviors due to the foliation structure of the spacetime geometry. We develop a frame covariant formalism of the toroidal geometry, which provides a geometrical interpretation of the recently discovered polynomial realization of SL(2 , ℤ) duality in nonrelativistic type IIB superstring theory. We will show that the nonrelativistic IIB string background fields transform as polynomials of an effective Galilean “boost velocity” on the two-torus. As an application, we construct an action principle describing a single M5-brane in nonrelativistic M-theory and study its compactification over the anisotropic two-torus. This procedure leads to a D3-brane action in nonrelativistic IIB string theory that makes the SL(2 , ℤ) invariance manifest in the polynomial realization.

Abstract The duality between type IIA superstring theory and M-theory enables us to lift bound states of D0-branes and n parallel D6-branes to M-theory compactified on an n-centered multi-Taub-NUT space TN $$ \mathbbm{TN} $$ n . Accordingly, the rank n K-theoretic Donaldson-Thomas invariants of ℂ3 are connected with the index of M-theory on ℂ3 × TN $$ \mathbbm{TN} $$ n . In this paper, we extend this connection by considering intersecting D6-branes. In the presence of a suitable Neveu-Schwarz B-field, the system preserves two supercharges. This system is T-dual to the configuration of tetrahedron instantons which we introduced in [1]. We conjecture a closed-form expression for the K-theoretic tetrahedron instanton partition function, which is the generating function of the D0-D6 partition functions. We find that the tetrahedron instanton partition function coincides with the partition function of the magnificent four model for special values of the parameters, leading us to conjecture that our system of intersecting D6-branes can be obtained from the annihilation of D8-branes and anti-D8-branes. Remarkably, the K-theoretic tetrahedron instanton partition function allows an interpretation in terms of the index of M-theory on a noncompact Calabi-Yau fivefold which is related to a superposition of Kaluza-Klein monopoles. The dimensional reduction of the system allows us to express the cohomological tetrahedron instanton partition function in terms of the MacMahon function, generalizing the correspondence between Gromov-Witten invariants and Donaldson-Thomas invariants for Calabi-Yau threefolds.

Abstract We recently described a protocol for computing the potential energy in heterotic M-theory for the dilaton, complex structure and Kähler moduli. This included the leading order non-perturbative contributions to the complex structure, gaugino condensation and worldsheet instantons assuming a hidden sector that contains an anomalous U(1) structure group embedded in E 8. In this paper, we elucidate, in detail, the mathematical and computational methods required to utilize this protocol. These methods are then applied to a realistic heterotic M-theory model, the B − L MSSM, whose observable sector is consistent with all particle physics requirements. Within this context, it is shown that the dilaton and universal moduli can be completely stabilized at values compatible with every phenomenological and mathematical constraint — as well as with ΛCDM cosmology. We also show that the heterotic M-theory vacua are consistent with all well-supported Swampland conjectures based on considerations of string theory and quantum gravity, and we discuss the implications of dark energy theorems for compactified theories.

Abstract We consider the uplift of co-dimension two defect solutions of seven dimensional gauged supergravity to eleven dimensions, previously found by two of the authors. The uplifted solutions are expressed as Lin-Lunin-Maldacena solutions and an infinite family of regular solutions describing holographic defects is found using the electrostatic formulation of LLM solutions.

Abstract The tower Weak Gravity Conjecture predicts infinitely many super-extremal states along every ray in the charge lattice of a consistent quantum gravity theory. We show this far-reaching claim in five-dimensional compactifications of M-theory on Calabi-Yau 3-folds for gauge groups with a weak coupling limit. We first characterize the possible weak coupling limits, building on an earlier classification of infinite distance limits in the Kähler moduli space of M-theory compactifications. We find that weakly coupled gauge groups are associated to curves on the compactification space contained in generic fibers or in fibers degenerating at finite distance in their moduli space. These always admit an interpretation as a Kaluza-Klein or winding U(1) in a dual frame or as part of a dual perturbative heterotic gauge group, in agreement with the Emergent String Conjecture. Using the connection between Donaldson-Thomas invariants and Noether-Lefschetz theory, we then show that every ray in the associated charge lattice either supports a tower of BPS states or of non-BPS states, and prove that these satisfy the super-extremality condition, at least in the weak coupling regime.

Abstract We continue the analysis of the geometry of generic Minkowski N $$ \mathcal{N} $$ = 1, D = 4 flux compactifications in M-theory using exceptional generalised geometry, including the calculation of the infinitesimal moduli spaces. The backgrounds can be classified into two classes: type-0 and type-3. For type-0, we review how the moduli arise from standard de Rham cohomology classes. We also argue that, under reasonable assumptions, there are no appropriate sources to support compact flux backgrounds for this class and so the only solutions are in fact G2 geometries. For type-3 backgrounds, given a suitable ∂ ′ ∂ ¯ ′ $$ {\partial}^{\prime }{\overline{\partial}}^{\prime } $$ -lemma, we show that the moduli can be calculated from a cohomology based on an involutive sub-bundle of the complexified tangent space. Using a simple spectral sequence we prove quite generally that the presence of flux can only reduce the number of moduli compared with the fluxless case. We then use the formalism to calculate the moduli of heterotic M-theory and show they match those of the dual Hull-Strominger system as expected.

Abstract We use the S-matrix bootstrap to carve out the space of unitary, analytic, crossing symmetric and supersymmetric graviton scattering amplitudes in nine, ten and eleven dimensions. We extend and improve the numerical methods of our previous work in ten dimensions. A key new tool employed here is unitarity in the celestial sphere. In all dimensions, we find that the minimal allowed value of the Wilson coefficient α, controlling the leading correction to maximal supergravity, is very close but not equal to the minimal value realized in Superstring theory or M-theory. This small difference may be related to inelastic effects that are not well described by our numerical extremal amplitudes. Although α has a unique value in M-theory, we found no evidence of an upper bound on α in 11D.

Abstract In this note, we resolve an apparent obstacle to string/M theory realizations of dS observer patch holography, finding a new role for averaging in quantum gravity. The solvable T T ¯ $$ T\overline{T} $$ (+Λ2) deformation recently provided a detailed microstate count of the dS 3 cosmic horizon, reproducing the refined Gibbons-Hawking entropy computed by Anninos et al. along with the correct radial bulk geometry. On the gravity side, the deformation brings in the boundary to just outside a black hole horizon, where it is indistinguishable from the dS cosmic horizon, enabling a continuous passage to a bounded patch of dS. In string/M theory, the relationship between AdS/CFT and dS involves uplifts that change the internal topology, e.g. replacing an internal sphere S $$ \mathbbm{S} $$ with an internal hyperbolic space ℍ (and incorporating varying warp and conformal factors). We connect these two approaches, noting that the differences in the extra dimensions between AdS black hole and dS solutions are washed out by internal averaging in the presence of a timelike boundary skirting the horizon. This helps to motivate a detailed investigation into the possibility of such timelike boundaries in (A)dS solutions of string/M theory, and we take initial steps toward suitable generalizations of Liouville walls as one approach.

Abstract We study electric-magnetic duality in compactifications of M-theory on twisted connected sum (TCS) G 2 manifolds via duality with F-theory. Specifically, we study the physics of the D3-branes in F-theory compactified on a Calabi-Yau fourfold Y, dual to a compactification of M-theory on a TCS G 2 manifold X. N $$ \mathcal{N} $$ = 2 supersymmetry is restored in an appropriate geometric limit. In that limit, we demonstrate that the dual of D3-branes probing seven-branes corresponds to the shrinking of certain surfaces and curves, yielding light particles that may carry both electric and magnetic charges. We provide evidence that the Minahan-Nemeschansky theories with E n flavor symmetry may be realized in this way. The SL(2, ℤ) monodromy of the 3/7-brane system is dual to a Fourier-Mukai transform of the dual IIA/M-theory geometry in this limit, and we extrapolate this monodromy action to the global compactification. Away from the limit, the theory is broken to N $$ \mathcal{N} $$ = 1 supersymmetry by a D-term.

Abstract We consider the most general solutions of eleven-dimensional supergravity preserving N = 2 supersymmetry whose metrics are warped products of three-dimensional anti-de Sitter space with an eight-dimensional manifold, focusing on those realising (2,0) superconformal symmetry. We give a set of necessary and sufficient conditions for a solution to be supersymmetric, which can be phrased, in the general case, in terms of a local SU(2) structure and its intrinsic torsion. We show that these supergravity backgrounds always admit a nowhere-vanishing Killing vector field that preserves the solution and encodes the U(1) R-symmetry of the dual field theory. We illustrate our results with examples which have appeared in the literature, including those with SU(4), G2 and SU(3) structures, and discuss new classes of Minkowski solutions.

Abstract It is argued that the supersymmetric index of a certain system of branes in M-theory is equal to the partition function of an integrable three-dimensional lattice model. The local Boltzmann weights of the lattice model satisfy a generalization of Zamolodchikov’s tetrahedron equation. In a special case the model is described by a solution of the tetrahedron equation discovered by Kapranov and Voevodsky and by Bazhanov and Sergeev.

In this study, it is aimed to investigate the Krori–Barua type compact stars within the scope of f(R, 픏m) theory. In this context, first, the field equations are obtained by considering the f(R, 픏m) = R 2 + α픏mn model. Interestingly, the model offers chance to attain all components of matter without any restrictions. In addition, data sets from LMC X-4, EXO 1785-248 and Cen X-3 are used to analyze physical stability of the solutions. It is obtained that all conditions such as causality and stability. which indicate consistency between compact objects and f(R, 픏m) theory are valid for the constructed model. We obtained that small values of n in the f(R, 픏m) function show significant effect on the consistency of the star models. Therefore, different n values are considered for each star data set when graphing the physical states. Finally, necessary quantities of the model are defined, compared with the considered stars and discussed in detail. [ABSTRACT FROM AUTHOR]

Abstract We study graviton scattering on AdS 4 × S 7, which is dual to the stress tensor multiplet four-point function in the maximally supersymmetric 3d U(N)1 × U(N) −1 ABJM theory. We compute 1-loop corrections to this holographic correlator coming from Witten diagrams with supergravity R and higher derivative R 4 vertices, up to contact term ambiguities, and find that the flat space limit matches the corresponding terms in the 11d M-theory S-matrix. We then use supersymmetric localization to show that all the 1-loop contact terms vanish, as was previously observed for the AdS 4 × S 7 /ℤ2 theory dual to U(N)2 × U(N) −2 ABJM. Finally, we use the recent localization results of Gaiotto and Abajian, as inspired by twisted M-theory, to compute all the short OPE coefficients in correlators of the stress tensor multiplet and the next lowest half-BPS operator, which we find saturate the bootstrap bounds on these mixed correlators for all N.

Abstract We classify rank zero 5d SCFTs geometrically engineered from M-theory on quasi-homogeneous compound Du Val isolated threefold singularities. For all such theories, we characterize the Higgs Branch, by computing the dimension, the continuous and discrete symmetry groups, as well as more refined details such as the charges of the hypermultiplets under these groups. We derive these data by means of a gauge-theoretic method, that we have recently introduced, based on establishing a correspondence between an adjoint Higgs field and the M-theory geometry. As a byproduct, this further allows us to construct several T-brane backgrounds, that yield inequivalent 5d spectra but are associated with the same geometry.

Soil particle size is an important indicator in soil systems, it can provide important assistance for the agricultural work. In order to address the weakness of traditional soil particle size measuring work, which are time-consuming, labor-intensive, and have limited applicability. This study utilizes the Mie theory and the Kubelka–Munk theory as the precondition, establish an empirical formula between the scattering power and the soil particle size. The study collected surface soil samples from Nong'an, Changchun City, Jilin Province, including black soil, brown soil, sandy soil, and each saline sample, based on visible and near-infrared spectroscopy. Prepare soil samples with a particle size range of 2.5–0.15 mm through drying, grinding, and sieving operations, combining scattering power parameters in the K-M theory to construct an empirical formula for it and soil particle. After verified by comparing different empirical formulas are suitable for the measured data, assume the inverse proportion formula added correction term is the most appropriate. The conclusion is there is a strong linear relationship between the scattering power and the reciprocal of particle size. The average fitting accuracy of the 400–2400 nm wavelength band reaches 94.45%, root mean square error ($\text{RMSE}$) reaches 0.0354 mm. After removing outliers, the fitting accuracy can reach up to 95.77%, $\text{RMSE}$up to 0.0337 mm. Proved there is a very high analytical relationship between soil particle size and scattering power parameters in K-M theory. The empirical formula also can find supported by Mie theory and S-shape R(D) function, and has a high transferability from the laboratory to Landsat8 satellite board, the accuracy can reach to about 90% on SWIR band, showed good generalization ability.

A universal structure of world-volume theories of 12-BPS branes in string and M-theory in terms of exceptional generalised geometry is observed. Previous constructions are extended in two ways: from internal d-dimensional space to full 11- or 10-dimensional spacetimes, by coupling to the tensor hierarchy gauge fields, and from Ed(d) with d≤6 to E7(7) and E8(8). This is done by a clarification of the role of the tensor hierarchy and its end in the context of brane world-volume theories. The exceptional structure of the gauged σ-model of the Kaluza-Klein monopole is provided as a new example.

Abstract We initiate a systematic analysis of the nonrelativistic membrane solutions of M theory using the notion of 11d membrane Newton-Cartan (MNC) geometry as well as considering a 1/c 2 expansion for the embedding fields of the M2 brane world-volume theory. We discuss the associated boost and dilatation symmetries of the nonrelativistic world-volume theory at leading order in the 1/c expansion. We show that, in the static gauge, when the world-volume directions of the nonrelativistic M2 brane are stretched along the longitudinal axes of the target space geometry, the leading order action in the 1/c expansion becomes trivial. In other words, the nontrivial dynamics appears to be only at NLO and beyond. In our analysis, we focus on such embeddings only and obtain the corresponding dispersion relation associated with the nonrelativistic world-volume theory.