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We show that coupling the SU(2)-valued Skyrme field to the ρ-meson solves the long-standing issue of (in)compressibility in the solitonic Skyrme model. Even by including only one ρπ interaction term, motivated by a holographic-like reduction of Yang-Mills action by Sutcliffe, reduces the compression modulus from K0 ≃ 1080 MeV, in the massive Skyrme model, to K0 ≃ 351 MeV. [ABSTRACT FROM AUTHOR]

We construct examples of non-invertible global symmetries in two-dimensional superconformal field theories described by sigma models into Calabi-Yau target spaces. Our construction provides some of the first examples of non-invertible symmetry in irrational conformal field theories. Our approach begins at a Gepner point in the conformal manifold where the sigma model specializes to a rational conformal field theory and we can identify all supersymmetric topological Verlinde lines. By deforming away from this special locus using exactly marginal operators, we then identify submanifolds in moduli space where some non-invertible symmetry persists. For instance, along ten-dimensional loci in the complex structure moduli space of quintic Calabi-Yau threefolds there is a symmetry characterized by a Fibonacci fusion category. The symmetries we identify provide new constraints on spectra and correlation functions. As an application we show how they constrain conformal perturbation theory, consistent with recent results about scaling dimensions in the K3 sigma model near its Gepner point. [ABSTRACT FROM AUTHOR]

In this paper, we study the scattering amplitudes and soft theorems for the sigma models with two scalars. We show that if the particles are Goldstone bosons, then you necessarily get Adler zero with no possibility for non-trivial soft theorems. For non-Goldstone bosons, the soft behavior is generically captured by the geometric soft theorem studied by Cheung et al., and the right-hand side contains derivatives of lower-point amplitudes. Inspired by the recent work on the 2D sigma models, we study one special two-scalar sigma model, where the presence of symmetries in the target space translates into a special but non-trivial soft theorem without derivatives. We further generalize the construction to two larger classes of such models and derive certain soft theorem sum rules, again avoiding the derivatives of amplitudes. Our analysis provides an interesting hierarchy of two-scalar sigma models and soft theorems, ranging from Goldstone boson case to a generic target space, and showing that there are interesting theories in between. [ABSTRACT FROM AUTHOR]

Abstract Not much is known about superstring scattering amplitudes in curved backgrounds. Using the hybrid formalism in AdS3 × S3 with pure NS-NS three-form flux, we compute a PSU(1, 1|2)-covariant three-point amplitude for half-BPS vertex operators inserted on the AdS3 boundary and show that it agrees with the RNS computation. The zero-mode prescription for the fermions in AdS is defined in terms of the “standard” spacetime SUSY generator. It is found that integrating out the fermionic worldsheet fields in the path integral gives rise to the target-space vielbein, which explicitly encodes that the conformal group on the boundary is identified with the symmetry group of the AdS bulk.

Abstract The ground state of QCD with two flavors (up and down quarks) at finite baryon density in sufficiently strong magnetic field is in a form of either a chiral soliton lattice(CSL), an array of solitons stacked along the magnetic field, or a domain-wall Skyrmion phase in which Skyrmions are spontaneously created on top of the CSL. In the latter, one 2D (baby) Skyrmion in the chiral soliton corresponds to two 3D Skyrmions (baryons) in the bulk. In this paper, we study spin statistics of topological solitons by using the following two methods: the conventional Witten’s method by embedding the pion fields of two flavors into those of three flavors with the Wess-Zumino-Witten (WZW) term, and a more direct method by using the two-flavor WZW term written in terms of a spin structure. We find that a chiral soliton of finite quantized size called a pancake soliton and a hole on a chiral soliton are fermions or bosons depending on odd or even quantizations of their surface areas, respectively, and a domain-wall Skyrmion is a boson. We also propose surgeries of topological solitons: a domain-wall Skyrmion (boson) can be cut into a pancake soliton (fermion) and a hole (fermion), and a chiral soliton without Skyrmions can be cut into a pancake soliton (fermion) and a hole (fermion).

Abstract We calculate the scattering amplitude in the two dimensional CP (1) model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. The results can be extended to the O(N) model, for all N. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories.

Abstract We supplement the string field theory action with boundary terms to make its variational principle well-posed. Central to our considerations is the violation of the stress-energy tensor conservation in non-compact CFTs due to the boundary terms. This manifests as the failure of the cyclicity of the BRST operator, which encodes the target space integration by parts identities at the level of the worldsheet. Using this failure, we argue that the free closed string field theory action admits a well-posed variational principle upon including an additional boundary contribution. We explicitly work out the resulting action up to the massless level and show that it is related to the expansion of the low-energy effective string action endowed with the Gibbons-Hawking-York term on a flat background. We also discuss the structure of the boundary terms in the interacting theory.

Abstract Supersymmetric field theories can be characterized by their Nicolai map, which is a nonlinear and nonlocal field transformation to their free-field limit. The systematic construction of such maps has recently been outlined for actions with power more than two in the fermions, which produces a perturbative expansion in loop-decorated fermionic tree diagrams. We thoroughly investigate the nonlinear ℂP 1 sigma model in (3+1)-dimensional Minkowski space as a paradigmatical example. We construct and test a chiral form of the Nicolai map, to third order in the coupling, including all (regularized) quantum parts. In addition, all trees with one or two edges are summed up. The free-action condition determines only the one-edge part of the map. We resolve the fermion loop decoration of the Nicolai trees by injecting an auxiliary vector field and present the ensuing classical Nicolai map to second order in a dimensionful coupling.

Abstract In contradistinction to the case of massive excitations, the connection between integrability and the tree-level massless scattering matrix of integrable σ-models is lost. Namely, in well-known 2-d integrable models the tree-level massless S-matrix exhibits particle production and fails to factorise. This is conjectured to happen due to IR ambiguities in the massless tree-level amplitudes. We present a definition of the massless S-matrix which has all the nice properties of integrable theories, there is no particle production and the S-matrix factorises. Our definition works for the large class of σ-models with one or more isometries. As an example, we present in detail the case of the SU(2) principal chiral model (PCM).

Abstract We generalize the auxiliary field deformations of the principal chiral model (PCM) introduced in [1] and [2] to sigma models whose target manifolds are symmetric or semi-symmetric spaces, including a Wess-Zumino term in the latter case. This gives rise to a new infinite family of classically integrable ℤ2 and ℤ4 coset models of the form which are of interest in applications of integrability to worldsheet string theory and holography. We demonstrate that every theory in this infinite class admits a zero-curvature representation for its equations of motion by exhibiting a Lax connection.

Abstract The JNR ansatz provides a simple formula to obtain families of charge N self-dual SU(2) Yang-Mills instantons in four-dimensional Euclidean space, from the free data of N + 1 distinct points with associated positive weights. Here an analogous formula is presented for Skyrme fields in three-dimensional Euclidean space. These families of Skyrme fields include good approximations to a range of Skyrmions, with energies that are typically within a few percent of the numerically computed solutions.

Abstract We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential μ at a fixed coupling of β. We determine the transition point μ c and the critical exponent ν from the μ dependence of the number density in the thermodynamic limit. The dynamical critical exponent z is also extracted from the scaling behavior of the temporal correlation length as a function of μ.

Abstract We study topological lumps supported by the second homotopy group π 2(S 2) ⋍ ℤ in a gauged O(3) model without any potential term coupled with a (non)dynamical U(1) gauge field. It is known that gauged-lumps are stable with an easy-plane potential term but are unstable to expand if the model has no potential term. In this paper, we find that these gauged lumps without a potential term can be made stable by putting them in a uniform magnetic field, irrespective of whether the gauge field is dynamical or not. In the case of the non-dynamical gauge field, only either of lumps or anti-lumps stably exists depending on the sign of the background magnetic field, and the other is unstable to shrink to be singular. We also construct coaxial multiple lumps whose size and mass exhibit a behaviour of droplets. In the case of the dynamical gauge field, both the lumps and anti-lumps stably exist with different masses; the lighter (heavier) one corresponds to the (un)stable one in the case of the nondynamical gauge field. We find that a lump behaves as a superconducting ring and traps magnetic field in its inside, with the total magnetic field reduced from the background magnetic field.

Abstract Perturbation theory in asymptotically free quantum field theories is asymptotic. The factorially growing perturbative coefficients carry information about non-perturbative corrections, which can be related to renormalons and instantons. Using the Wiener-Hopf technique we determine the full analytic solution for the free energy density in the two dimensional O(N) sigma models. For N > 3 there are no instantons, and we found that the perturbative series carries all the information about the non-perturbative corrections. However, in the O(3) case, we identify several non-perturbative sectors that are not related to the asymptotics of the perturbative series. The number of sectors depends on the observables: for the ground-state energy density we identify three sectors, which we attribute to instantons. For the free energy density in the running perturbative coupling we found infinitely many sectors.

Abstract We prove the existence of a family of integrable deformations of ℤ N -coset models in two dimensions. Our approach uses and generalises the method of auxiliary fields that was recently introduced for the principal chiral model by Ferko and Smith.

Abstract This paper presents a new perspective on integrability in theories of gravity. We show how the stationary, axisymmetric sector of General Relativity can be described by the boundary dynamics of a four-dimensional Chern-Simons theory. This approach shows promise for simplifying solution generating methods in both General Relativity and higher-dimensional supergravity theories. The four-dimensional Chern-Simons theory presented generalises those for flat space integrable models by introducing a space-time dependent branch cut in the spectral plane. We also make contact with twistor space approaches to integrability, showing how the branch cut defects of four-dimensional Chern-Simons theory arise from a discrete reduction of six-dimensional Chern-Simons theory.

Abstract We study the worldsheet CFTs of type II strings on compact G 2 orbifolds obtained as quotients of a product of a Calabi-Yau threefold and a circle. For such models, we argue that the Calabi-Yau mirror map implies a mirror map for the associated G 2 varieties by examining how anti-holomorphic involutions behave under Calabi-Yau mirror symmetry. The mirror geometries identified by the worldsheet CFT are consistent with earlier proposals for twisted connected sum G 2 manifolds.

Abstract In this letter we use a perturbative approach to find the spectrum of non-relativistic strings in the String Newton-Cartan (SNC) AdS5×S5 spacetime. We perturb the bosonic sector of the action around a BMN-like folded string solution in light-cone gauge. We find strong evidence that the theory is described by a combination of massive and massless free fields in an anti-de Sitter background by showing that interaction terms up to six scalars vanish after field redefinitions.

Abstract We highlight the need for global completion of the field content in the M5-brane sigma-model analogous to Dirac’s charge/flux quantization, and we point out that the superspace Bianchi identities on the worldvolume and on its ambient supergravity background constrain the M5’s flux-quantization law to be in a non-abelian cohomology theory rationally equivalent to a twisted form of co-Homotopy. In order to clearly bring out this subtle point we give a streamlined re-derivation of the worldvolume 3-flux via M5 “super-embeddings”. Finally, assuming the flux-quantization law to actually be in co-Homotopy (“Hypothesis H”) we show how this implies Skyrmion-like solitons on general M5-worldvolumes and (abelian) anyonic solitons on the boundaries of “open M5-branes” in heterotic M-theory.

Motivated from target space covariant formulations of topological sigma models and from a graded-geometric approach to higher gauge theory, we study connections on Lie and Courant algebroids and on their description as differential graded (dg) manifolds. We revisit the notion of basic curvature for a connection on a Lie algebroid, which measures its compatibility with the Lie bracket and it appears in the BV-BRST differential of 2D gauge theories such as (twisted) Poisson and Dirac sigma models. We define a basic curvature tensor for connections on Courant algebroids and we show that in the description of a Courant algebroid as a QP2 manifold it appears naturally as part of the homological vector field together with the Gualtieri torsion of an induced generalised connection. Furthermore, we consider connections on dg manifolds and revisit the structure of gauge transformations in the graded-geometric approach to higher gauge theories from a manifestly covariant perspective. We argue that it is governed by the brackets of a Kapranov L ∞ [ 1 ] algebra, whose binary bracket is given by the Atiyah cocycle that measures the compatibility of the connection with the homological vector field. We also revisit some aspects of the derived bracket construction and show how to extend it to connections and tensors. [ABSTRACT FROM AUTHOR]

The JNR ansatz provides a simple formula to obtain families of charge N self-dual SU(2) Yang-Mills instantons in four-dimensional Euclidean space, from the free data of N + 1 distinct points with associated positive weights. Here an analogous formula is presented for Skyrme fields in three-dimensional Euclidean space. These families of Skyrme fields include good approximations to a range of Skyrmions, with energies that are typically within a few percent of the numerically computed solutions. [ABSTRACT FROM AUTHOR]

We study the quantum phase transition of the (1+1)-dimensional O(3) nonlinear sigma model at finite density using the tensor renormalization group method. This model suffers from the sign problem, which has prevented us from investigating the properties of the phase transition. We investigate the properties of the phase transition by changing the chemical potential μ at a fixed coupling of β. We determine the transition point μc and the critical exponent ν from the μ dependence of the number density in the thermodynamic limit. The dynamical critical exponent z is also extracted from the scaling behavior of the temporal correlation length as a function of μ. [ABSTRACT FROM AUTHOR]

We study topological lumps supported by the second homotopy group π2(S2) ⋍ ℤ in a gauged O(3) model without any potential term coupled with a (non)dynamical U(1) gauge field. It is known that gauged-lumps are stable with an easy-plane potential term but are unstable to expand if the model has no potential term. In this paper, we find that these gauged lumps without a potential term can be made stable by putting them in a uniform magnetic field, irrespective of whether the gauge field is dynamical or not. In the case of the non-dynamical gauge field, only either of lumps or anti-lumps stably exists depending on the sign of the background magnetic field, and the other is unstable to shrink to be singular. We also construct coaxial multiple lumps whose size and mass exhibit a behaviour of droplets. In the case of the dynamical gauge field, both the lumps and anti-lumps stably exist with different masses; the lighter (heavier) one corresponds to the (un)stable one in the case of the nondynamical gauge field. We find that a lump behaves as a superconducting ring and traps magnetic field in its inside, with the total magnetic field reduced from the background magnetic field. [ABSTRACT FROM AUTHOR]

Perturbation theory in asymptotically free quantum field theories is asymptotic. The factorially growing perturbative coefficients carry information about non-perturbative corrections, which can be related to renormalons and instantons. Using the Wiener-Hopf technique we determine the full analytic solution for the free energy density in the two dimensional O(N) sigma models. For N > 3 there are no instantons, and we found that the perturbative series carries all the information about the non-perturbative corrections. However, in the O(3) case, we identify several non-perturbative sectors that are not related to the asymptotics of the perturbative series. The number of sectors depends on the observables: for the ground-state energy density we identify three sectors, which we attribute to instantons. For the free energy density in the running perturbative coupling we found infinitely many sectors. [ABSTRACT FROM AUTHOR]

We prove the existence of a family of integrable deformations of ℤN-coset models in two dimensions. Our approach uses and generalises the method of auxiliary fields that was recently introduced for the principal chiral model by Ferko and Smith. [ABSTRACT FROM AUTHOR]

We highlight the need for global completion of the field content in the M5-brane sigma-model analogous to Dirac’s charge/flux quantization, and we point out that the superspace Bianchi identities on the worldvolume and on its ambient supergravity background constrain the M5’s flux-quantization law to be in a non-abelian cohomology theory rationally equivalent to a twisted form of co-Homotopy. In order to clearly bring out this subtle point we give a streamlined re-derivation of the worldvolume 3-flux via M5 “super-embeddings”. Finally, assuming the flux-quantization law to actually be in co-Homotopy (“Hypothesis H”) we show how this implies Skyrmion-like solitons on general M5-worldvolumes and (abelian) anyonic solitons on the boundaries of “open M5-branes” in heterotic M-theory. [ABSTRACT FROM AUTHOR]

In this letter we use a perturbative approach to find the spectrum of non-relativistic strings in the String Newton-Cartan (SNC) AdS5×S5 spacetime. We perturb the bosonic sector of the action around a BMN-like folded string solution in light-cone gauge. We find strong evidence that the theory is described by a combination of massive and massless free fields in an anti-de Sitter background by showing that interaction terms up to six scalars vanish after field redefinitions. [ABSTRACT FROM AUTHOR]

We study the worldsheet CFTs of type II strings on compact G2 orbifolds obtained as quotients of a product of a Calabi-Yau threefold and a circle. For such models, we argue that the Calabi-Yau mirror map implies a mirror map for the associated G2 varieties by examining how anti-holomorphic involutions behave under Calabi-Yau mirror symmetry. The mirror geometries identified by the worldsheet CFT are consistent with earlier proposals for twisted connected sum G2 manifolds. [ABSTRACT FROM AUTHOR]

This paper presents a new perspective on integrability in theories of gravity. We show how the stationary, axisymmetric sector of General Relativity can be described by the boundary dynamics of a four-dimensional Chern-Simons theory. This approach shows promise for simplifying solution generating methods in both General Relativity and higher-dimensional supergravity theories. The four-dimensional Chern-Simons theory presented generalises those for flat space integrable models by introducing a space-time dependent branch cut in the spectral plane. We also make contact with twistor space approaches to integrability, showing how the branch cut defects of four-dimensional Chern-Simons theory arise from a discrete reduction of six-dimensional Chern-Simons theory. [ABSTRACT FROM AUTHOR]

Abstract We study the beta deformation of the superstring in AdS 5 × S 5 at all orders in the deformation parameter, employing the pure spinor formalism. This is necessary in order to study the regime of strong deformation parameter, which in the field side is related to fishnet theories. We compare the pure spinor sigma model approach to the previously known supergravity description. We find a complete agreement. Moreover, the BRST structure of the worldsheet model provides a natural explanation of the peculiar features of the worldsheet model in the fishnet limit. In particular, we study the degeneracy of the sigma model Lagrangian. We show that the BRST structure is responsible for a particularly “tame” degeneration of the fishnet sigma-model.

Abstract Motivated by the two-dimensional massive gravity description of T T ¯ $$ T\overline{T} $$ deformations, we propose a direct generalization in d dimensions. Our methodology indicates that all terms up to order d are present in the deformation. In two dimensions, T T ¯ $$ T\overline{T} $$ is enhanced by a linear and a constant term, and exhibits an interesting behaviour regarding the deformed spectrum and correlators. At certain limits, this deformation can reduce to T T ¯ $$ T\overline{T} $$ or T T ¯ $$ T\overline{T} $$ + Λ2 consistently. Using the massive gravity method, we obtain the classically deformed action of a sigma model of bosons and fermions interacting with an arbitrary potential, extending previous results. As a consequence, a proposal regarding the deformation of higher-derivative theories is made. Moreover, a standard dimensional reduction procedure is presented, with the resulting operator matching the form of prior findings under certain assumptions. In d ≥ 2, we provide the exact structure of the quadratic terms in agreement with previous approaches, as well as the structure of the linear and constant terms. All higher order contributions are not easily evaluated, yet we derive the complete answer for all cases up to seven dimensions. Under certain conditions, these terms vanish, resulting in a quadratic operator. The trace-flow equation for this family of deformations is also derived. Finally, we investigate the class of root- T T ¯ $$ T\overline{T} $$ operators in various dimensions within the scope of this formalism.

Abstract We revisit the flavored elliptic genus of the N=2 superconformal cigar model and generalize the analysis of the path integral result to the case of real central charge. It gives rise to a non-holomorphic modular covariant function generalizing completed mock modular forms. We also compute the genus for angular orbifolds of the cigar and Liouville theory and decompose it in terms of discrete and continuous contributions. The orbifolded elliptic genus at fractional level is a completed mock modular form with a shadow related to U(1) modular invariants at rational radius squared. We take the limit of the orbifolded genera towards a weighted ground state index and carefully interpret the contributions. We stress that the orbifold cigar and Liouville theories have a maximal and a minimal radius, respectively.

Abstract We draw a parallel between the BV/BRST formalism for higher-dimensional (≥ 2) Hamiltonian mechanics and higher notions of torsion and basic curvature tensors for generalized connections in specific Lie n-algebroids based on homotopy Poisson structures. The gauge systems we consider include Poisson sigma models in any dimension and “generalised R-flux” deformations thereof, such as models with an (n + 2)-form-twisted R-Poisson target space. Their BV/BRST action includes interaction terms among the fields, ghosts and antifields whose coefficients acquire a geometric meaning by considering twisted Koszul multibrackets that endow the target space with a structure that we call a gapped almost Lie n-algebroid. Studying covariant derivatives along n-forms, we define suitable polytorsion and basic polycurvature tensors and identify them with the interaction coefficients in the gauge theory, thus relating models for topological n-branes to differential geometry on Lie n-algebroids.

Abstract For the class of 1 + 1 dimensional field theories referred to as the non-linear sigma models, there is known to be a deep connection between classical integrability and one-loop renormalizability. In this work, the phenomenon is reviewed on the example of the so-called fully anisotropic SU(2) Principal Chiral Field (PCF). Along the way, we discover a new classically integrable four parameter family of sigma models, which is obtained from the fully anisotropic SU(2) PCF by means of the Poisson-Lie deformation. The theory turns out to be one-loop renormalizable and the system of ODEs describing the flow of the four couplings is derived. Also provided are explicit analytical expressions for the full set of functionally independent first integrals (renormalization group invariants).

Abstract We study twisted Courant sigma models, a class of topological field theories arising from the coupling of 3D 0-/2-form BF theory and Chern-Simons theory and containing a 4-form Wess-Zumino term. They are examples of theories featuring a nonlinearly open gauge algebra, where products of field equations appear in the commutator of gauge transformations, and they are reducible gauge systems. We determine the solution to the master equation using a technique, the BRST power finesse, that combines aspects of the AKSZ construction (which applies to the untwisted model) and the general BV-BRST formalism. This allows for a geometric interpretation of the BV coefficients in the interaction terms of the master action in terms of an induced generalised connection on a 4-form twisted (pre-)Courant algebroid, its Gualtieri torsion and the basic curvature tensor. It also produces a frame independent formulation of the model. We show, moreover, that the gauge fixed action is the sum of the classical one and a BRST commutator, as expected from a Schwarz type topological field theory.

Motivated by the two-dimensional massive gravity description of T T ¯ deformations, we propose a direct generalization in d dimensions. Our methodology indicates that all terms up to order d are present in the deformation. In two dimensions, T T ¯ is enhanced by a linear and a constant term, and exhibits an interesting behaviour regarding the deformed spectrum and correlators. At certain limits, this deformation can reduce to T T ¯ or T T ¯ + Λ2 consistently. Using the massive gravity method, we obtain the classically deformed action of a sigma model of bosons and fermions interacting with an arbitrary potential, extending previous results. As a consequence, a proposal regarding the deformation of higher-derivative theories is made. Moreover, a standard dimensional reduction procedure is presented, with the resulting operator matching the form of prior findings under certain assumptions. In d ≥ 2, we provide the exact structure of the quadratic terms in agreement with previous approaches, as well as the structure of the linear and constant terms. All higher order contributions are not easily evaluated, yet we derive the complete answer for all cases up to seven dimensions. Under certain conditions, these terms vanish, resulting in a quadratic operator. The trace-flow equation for this family of deformations is also derived. Finally, we investigate the class of root- T T ¯ operators in various dimensions within the scope of this formalism. [ABSTRACT FROM AUTHOR]

We study the beta deformation of the superstring in AdS5 × S5 at all orders in the deformation parameter, employing the pure spinor formalism. This is necessary in order to study the regime of strong deformation parameter, which in the field side is related to fishnet theories. We compare the pure spinor sigma model approach to the previously known supergravity description. We find a complete agreement. Moreover, the BRST structure of the worldsheet model provides a natural explanation of the peculiar features of the worldsheet model in the fishnet limit. In particular, we study the degeneracy of the sigma model Lagrangian. We show that the BRST structure is responsible for a particularly “tame” degeneration of the fishnet sigma-model. [ABSTRACT FROM AUTHOR]

For the class of 1 + 1 dimensional field theories referred to as the non-linear sigma models, there is known to be a deep connection between classical integrability and one-loop renormalizability. In this work, the phenomenon is reviewed on the example of the so-called fully anisotropic SU(2) Principal Chiral Field (PCF). Along the way, we discover a new classically integrable four parameter family of sigma models, which is obtained from the fully anisotropic SU(2) PCF by means of the Poisson-Lie deformation. The theory turns out to be one-loop renormalizable and the system of ODEs describing the flow of the four couplings is derived. Also provided are explicit analytical expressions for the full set of functionally independent first integrals (renormalization group invariants). [ABSTRACT FROM AUTHOR]

We draw a parallel between the BV/BRST formalism for higher-dimensional (≥ 2) Hamiltonian mechanics and higher notions of torsion and basic curvature tensors for generalized connections in specific Lie n-algebroids based on homotopy Poisson structures. The gauge systems we consider include Poisson sigma models in any dimension and “generalised R-flux” deformations thereof, such as models with an (n + 2)-form-twisted R-Poisson target space. Their BV/BRST action includes interaction terms among the fields, ghosts and antifields whose coefficients acquire a geometric meaning by considering twisted Koszul multibrackets that endow the target space with a structure that we call a gapped almost Lie n-algebroid. Studying covariant derivatives along n-forms, we define suitable polytorsion and basic polycurvature tensors and identify them with the interaction coefficients in the gauge theory, thus relating models for topological n-branes to differential geometry on Lie n-algebroids. [ABSTRACT FROM AUTHOR]

We revisit the flavored elliptic genus of the N=2 superconformal cigar model and generalize the analysis of the path integral result to the case of real central charge. It gives rise to a non-holomorphic modular covariant function generalizing completed mock modular forms. We also compute the genus for angular orbifolds of the cigar and Liouville theory and decompose it in terms of discrete and continuous contributions. The orbifolded elliptic genus at fractional level is a completed mock modular form with a shadow related to U(1) modular invariants at rational radius squared. We take the limit of the orbifolded genera towards a weighted ground state index and carefully interpret the contributions. We stress that the orbifold cigar and Liouville theories have a maximal and a minimal radius, respectively. [ABSTRACT FROM AUTHOR]

We study twisted Courant sigma models, a class of topological field theories arising from the coupling of 3D 0-/2-form BF theory and Chern-Simons theory and containing a 4-form Wess-Zumino term. They are examples of theories featuring a nonlinearly open gauge algebra, where products of field equations appear in the commutator of gauge transformations, and they are reducible gauge systems. We determine the solution to the master equation using a technique, the BRST power finesse, that combines aspects of the AKSZ construction (which applies to the untwisted model) and the general BV-BRST formalism. This allows for a geometric interpretation of the BV coefficients in the interaction terms of the master action in terms of an induced generalised connection on a 4-form twisted (pre-)Courant algebroid, its Gualtieri torsion and the basic curvature tensor. It also produces a frame independent formulation of the model. We show, moreover, that the gauge fixed action is the sum of the classical one and a BRST commutator, as expected from a Schwarz type topological field theory. [ABSTRACT FROM AUTHOR]

Abstract The scattering of gluons and gravitons in trivial backgrounds is endowed with many surprising infrared features which have interesting conformal interpretations on the two-dimensional celestial sphere. However, the fate of these structures in more general asymptotically flat backgrounds is far from clear. In this paper, we consider holomorphic infrared structures in the presence of non-perturbative, self-dual background gauge and gravitational fields which are determined by freely specified radiative data. We make use of explicit formulae for tree-level gluon and graviton scattering in these self-dual radiative backgrounds, as well as chiral twistor sigma model descriptions of the classical dynamics. Remarkably, we find that the leading holomorphic part of tree-level collinear splitting functions — or celestial OPEs — and infinite-dimensional chiral soft algebras are undeformed by the background. We also compute all-order holomorphic celestial OPEs in the MHV sectors of gauge theory and gravity.

Abstract The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field theory in a bounded manifold one needs to restrict the path integration domain of the point-particle to a specific subset of worldlines enclosed by those boundaries. In the present article it is shown how to implement this restriction for the case of a spinor field in a two-dimensional curved half-plane under MIT bag boundary conditions, and compute the first few heat-kernel coefficients as a verification of the proposed construction. This construction admits several generalisations.

Abstract We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the one-particle-irreducible effective action. The form of the recursion relation resembles the operation of raising the rank of a tensor by acting with a covariant derivative. This inspires a geometric interpretation, whose features and flaws we investigate.

Abstract In the context of supersymmetric quantum mechanics we formulate new supersymmetric localization principle, with application to trace formulas for a full thermal partition function. Unlike the standard localization principle, this new principle allows to compute the supertrace of non-supersymmetric observables, and is based on the existence of fermionic zero modes. We describe corresponding new invariant supersymmetric deformations of the path integral; they differ from the standard deformations arising from the circle action and require higher derivatives terms. Consequently, we prove that the path integral localizes to periodic orbits and not only on constant ones. We illustrate the principle by deriving bosonic trace formulas on compact Lie groups, including classical Jacobi inversion formula.

Abstract The spectral flow is ubiquitous in the physics of soliton-fermion interacting systems. We study the spectral flows related to a continuous deformation of background soliton solutions, which enable us to develop insight into the emergence of fermionic zero modes and the localization mechanism of fermion densities. We investigate a ℂP2 nonlinear sigma model in which there are the (anti-) instantons and also the sphalerons with vanishing topological charge. The standard Yukawa coupling of the fermion successfully generates infinite towers of the spectra and the spectral flow is observed when increasing the size of such solitons. At that moment, the localization of the fermions on the solitons emerges. The avoided crossings are also observed in several stages of the exchange of the flows, they are indicating a manifestation of the fermion exchange of the localizing nature.

Abstract In the past few years, the unifying frameworks of 4-dimensional Chern-Simons theory and affine Gaudin models have allowed for the systematic construction of a large family of integrable σ-models. These models depend on the data of a Riemann surface C (here of genus 0 or 1) and of a meromorphic 1-form ω on C, which encodes the geometry of their spectral parameter and the analytic structure of their Lax connection. The main subject of this paper is the renormalisation of these theories and in particular two conjectures describing their 1-loop RG-flow in terms of the 1-form ω. These conjectures were put forward in [1] and [2] and were proven in a variety of cases. After extending the proposal of [1] to the elliptic setup (with C of genus 1), we establish the equivalence of these two conjectures and discuss some of their applications. Moreover, we check their veracity on an explicit example, namely an integrable elliptic deformation of the Principal Chiral Model on $${{\text{SL}}}_{\mathbb{R}}\left(N\right)$$ .

Abstract We introduce a classical fractional particle model in ℝ n , extending the Newtonian particle concept with the incorporation of the fractional Laplacian. A comprehensive discussion on kinetic properties, including linear momentum and kinetic energy, is provided. We further derive the equations of motion and discuss the symmetries of the system. The Green’s function method is employed to solve the equations of motion in a general case. We illustrate the theory with three important examples: the free fractional particle, the fractional harmonic oscillator, and the charged fractional particle that interacts locally with the electromagnetic field. We use the results of the extension problem by Caffarelli and Silvestre, to construct the associated classical local sigma model for the fractional particle. The sigma model is then quantized using the canonical quantization method, and we compute the vacuum energy at the boundary.

Abstract Superconformal ‘type B’ quantum mechanical sigma models arise in a variety of interesting contexts, such as the description of D-brane bound states in an AdS2 decoupling limit. Focusing on N = 2B models, we study superconformal indices which count short multiplets and provide an alternative to the standard Witten index, as the latter suffers from infrared issues. We show that the basic index receives contributions from lowest Landau level states in an effective magnetic field and that, due to the noncompactness of the target space, it is typically divergent. Fortunately, the models of interest possess an additional target space isometry which allows for the definition of a well-behaved refined index. We compute this index using localization of the functional integral and find that the result agrees with a naive application of the Atiyah-Bott fixed point formula outside of it’s starting assumptions. In the simplest examples, this formula can also be directly verified by explicitly computing the short multiplet spectrum.