Search

Abstract This paper develops an enlarged BRST framework to treat the large gauge transformations of a given quantum field theory. It determines the associated infinitely many Noether charges stemming from a gauge fixed and BRST invariant Lagrangian, a result that cannot be obtained from Noether’s second theorem. The geometrical significance of this result is highlighted by the construction of a trigraded BRST covariant phase space, allowing a BRST invariant gauge fixing procedure. This provides an appropriate framework for determining the conserved BRST Noether current of the global BRST symmetry and the associated global Noether charges. The latter are found to be equivalent with the usual classical corner charges of large gauge transformations. It allows one to prove the gauge independence of their physical effects at the perturbative quantum level. In particular, the underlying BRST fundamental canonical relation provides the same graded symplectic brackets as in the classical covariant phase space. A unified Lagrangian Ward identity for small and large gauge transformations is built. It consistently decouples into a bulk part for small gauge transformations, which is the standard BRST-BV quantum master equation, and a boundary part for large gauge transformations. The boundary part provides a perturbation theory origin for the invariance of the Hamiltonian physical -matrix under asymptotic symmetries. Holographic anomalies for the boundary Ward identity are studied and found to be solutions of a codimension one Wess-Zumino consistency condition. Such solutions are studied in the context of extended BMS symmetry. Their existence clarifies the status of the 1-loop correction to the subleading soft graviton theorem.

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 We give an interpretation of holography in the form of the AdS/CFT correspondence in terms of homotopy algebras. A field theory such as a bulk gravity theory can be viewed as a homotopy Lie or L ∞ algebra. We extend this dictionary to theories defined on manifolds with a boundary, including the conformal boundary of AdS, taking into account the cyclic structure needed to define an action with the correct boundary terms. Projecting fields to their boundary values then defines a homotopy retract, which in turn implies that the cyclic L ∞ algebra of the bulk theory is equivalent, up to homotopy, to a cyclic L ∞ algebra on the boundary. The resulting action is the ‘on-shell action’ conventionally computed via Witten diagrams that, according to AdS/CFT, yields the generating functional for the correlation functions of the dual CFT. These results are established with the help of new techniques regarding the homotopy transfer of cyclic L ∞ algebras.

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 Asymptotic observables in quantum field theory beyond the familiar S-matrix have recently attracted much interest, for instance in the context of gravity waveforms. Such observables can be understood in terms of Schwinger-Keldysh-type ‘amplitudes’ computed by a set of modified Feynman rules involving cut internal legs and external legs labelled by time-folds. In parallel, a homotopy-algebraic understanding of perturbative quantum field theory has emerged in recent years. In particular, passing through homotopy transfer, the S-matrix of a perturbative quantum field theory can be understood as the minimal model of an associated (quantum) L ∞ -algebra. Here we bring these two developments together. In particular, we show that Schwinger-Keldysh amplitudes are naturally encoded in an L ∞ -algebra, similar to ordinary scattering amplitudes. As before, they are computed via homotopy transfer, but using deformation-retract data that are not canonical (in contrast to the conventional S-matrix). We further show that the L ∞ -algebras encoding Schwinger-Keldysh amplitudes and ordinary amplitudes are quasi-isomorphic (meaning, in a suitable sense, equivalent). This entails a set of recursion relations that enable one to compute Schwinger-Keldysh amplitudes in terms of ordinary amplitudes or vice versa.

Abstract Two dimensional gauge theories with charged matter fields are useful toy models for studying gauge theory dynamics, and in particular for studying the duality of large N gauge theories to perturbative string theories. A useful starting point for such studies is the pure Yang-Mills theory, which is exactly solvable. Its 1/N expansion was interpreted as a string theory by Gross and Taylor 30 years ago, but they did not provide a worldsheet action for this string theory, and such an action is useful for coupling it to matter fields. The chiral sector of the Yang-Mills theory can be written as a sum over holomorphic maps and has useful worldsheet descriptions, but the full theory includes more general extremal-area maps; a formal worldsheet action including all these maps in a “topological rigid string theory” was written by Hořava many years ago, but various subtleties arise when trying to use it for computations. In this paper we suggest a Polyakov-like generalization of Hořava’s worldsheet action which is well-defined, and we show how it reproduces the free limit of the Yang-Mills theory, both by formal arguments and by explicitly computing its partition function in several cases. In the future we plan to generalize this string theory to the finite-coupling gauge theory, and to analyze it with boundaries, corresponding either to Wilson loops or to dynamical matter fields in the fundamental representation.

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.

Abstract Gradient Flow Exact Renormalization Group (GF-ERG) is a framework to define the renormalization group flow of Wilsonian effective action utilizing coarse-graining along the diffusion equations. We apply it for Scalar Quantum Electrodynamics and derive flow equations for the Wilsonian effective action with the perturbative expansion in the gauge coupling. We focus on the quantum corrections to the correlation functions up to the second order of the gauge coupling and discuss the gauge invariance of the GF-ERG flow. We demonstrate that the anomalous dimension of the gauge field agrees with the standard perturbative computation and that the mass of the photon keeps vanishing in general spacetime dimensions. The latter is a noteworthy fact that contrasts with the conventional Exact Renormalization Group formalism in which an artificial photon mass proportional to a cutoff scale is induced. Our results imply that the GF-ERG can give a gauge-invariant renormalization group flow in a non-perturbative way.

Abstract We consider the 4-dimensional N $$ \mathcal{N} $$ = 1 Lie superconformal algebra and search for completely “symmetric” (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant polynomial cubic in the generalized curvatures of superconformal gravity vanishes. Consequently, the associated Chern-Simons polynomial is a non-trivial anomaly cocycle. We explicitly compute this cocycle to all orders in the independent fields of superconformal gravity and establish that it is BRST equivalent to the so-called superconformal a-anomaly. We briefly discuss the possibility that the superconformal c-anomaly also admits a similar Chern-Simons formulation and the potential holographic, 5-dimensional, interpretation of our results.

Gradient Flow Exact Renormalization Group (GF-ERG) is a framework to define the renormalization group flow of Wilsonian effective action utilizing coarse-graining along the diffusion equations. We apply it for Scalar Quantum Electrodynamics and derive flow equations for the Wilsonian effective action with the perturbative expansion in the gauge coupling. We focus on the quantum corrections to the correlation functions up to the second order of the gauge coupling and discuss the gauge invariance of the GF-ERG flow. We demonstrate that the anomalous dimension of the gauge field agrees with the standard perturbative computation and that the mass of the photon keeps vanishing in general spacetime dimensions. The latter is a noteworthy fact that contrasts with the conventional Exact Renormalization Group formalism in which an artificial photon mass proportional to a cutoff scale is induced. Our results imply that the GF-ERG can give a gauge-invariant renormalization group flow in a non-perturbative way. [ABSTRACT FROM AUTHOR]

We consider the 4-dimensional N = 1 Lie superconformal algebra and search for completely "symmetric" (in the graded sense) 3-index invariant tensors. The solution we find is unique and we show that the corresponding invariant polynomial cubic in the generalized curvatures of superconformal gravity vanishes. Consequently, the associated Chern-Simons polynomial is a non-trivial anomaly cocycle. We explicitly compute this cocycle to all orders in the independent fields of superconformal gravity and establish that it is BRST equivalent to the so-called superconformal a-anomaly. We briefly discuss the possibility that the superconformal c-anomaly also admits a similar Chern-Simons formulation and the potential holographic, 5-dimensional, interpretation of our results. [ABSTRACT FROM AUTHOR]

Abstract The double copy is a remarkable relationship between gauge theory and gravity that has been explored in a number of contexts, most notably scattering amplitudes and classical solutions. The convolutional double copy provides a straightforward method to bridge the two theories via a precise map for the fields and symmetries at the linearised level. This method has been thoroughly investigated in flat space, offering a comprehensive dictionary both with and without fixing the gauge degrees of freedom. In this paper, we extend this to curved space with an (anti) de Sitter background metric. We work in the temporal gauge, and employ a modified convolution that involves the Mellin transformation in the time direction. As an example, we show that the point-like charge in gauge theory double copies to the (dS-) Schwarzschild black hole solution.

Abstract We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the harmonic oscillator to finite-dimensional phase space. This induces a homotopy transfer from the BV algebra to the algebra of functions on phase space. Quantum expectation values for a given operator or functional are computed by the function whose pullback gives a functional in the same cohomology class. This statement is proved in perturbation theory by relating the perturbation lemma to Wick’s theorem. We test this method by computing two-point functions for the harmonic oscillator for position eigenstates and coherent states. Finally, we derive the Unruh effect, illustrating that these methods are applicable to quantum field theory.

Abstract In this work we present a complete three-loop renormalisation of an abelian chiral gauge theory within the Breitenlohner-Maison/’t Hooft-Veltman (BMHV) scheme of dimensional regularisation (DReg). In this scheme the γ 5-matrix appearing in gauge interactions is a non-anticommuting object, leading to a breaking of gauge and BRST invariance. Employing an efficient method based on the quantum action principle, we obtain the complete three-loop counterterm action which serves both to render the theory finite and to restore gauge and BRST invariance. The UV singular counterterms involve not only higher order ϵ-poles but also new counterterm structures emerging at the three-loop level for the first time; the finite symmetry-restoring counterterms are restricted to the same structures as at lower loop orders, just with different coefficients, aligning with our expectations. Both the singular and the finite counterterms include structures which cannot be obtained by the standard multiplicative renormalisation. Our results demonstrate that a rigorous treatment of chiral gauge theories with γ 5 defined in the BMHV scheme at the multi-loop level is possible and that the obtained counterterm action is suitable for computer implementations, allowing automated calculations without ambiguities caused by γ 5.

Abstract We present the manifestly covariant canonical operator formalism of a Weyl invariant (or equivalently, a locally scale invariant) gravity whose classical action consists of the well-known conformal gravity and Weyl invariant scalar-tensor gravity, on the basis of the Becchi-Rouet-Stora-Tyupin (BRST) formalism. It is shown that there exists a Poincaré-like IOSp(8|8) global symmetry as in Einstein’s general relativity, which should be contrasted to the case of only the Weyl invariant scalar-tensor gravity where we have a more extended Poincaré-like IOSp(10|10) global symmetry. This reduction of the global symmetry is attributed to the presence of the Stückelberg symmetry.

The double copy is a remarkable relationship between gauge theory and gravity that has been explored in a number of contexts, most notably scattering amplitudes and classical solutions. The convolutional double copy provides a straightforward method to bridge the two theories via a precise map for the fields and symmetries at the linearised level. This method has been thoroughly investigated in flat space, offering a comprehensive dictionary both with and without fixing the gauge degrees of freedom. In this paper, we extend this to curved space with an (anti) de Sitter background metric. We work in the temporal gauge, and employ a modified convolution that involves the Mellin transformation in the time direction. As an example, we show that the point-like charge in gauge theory double copies to the (dS-) Schwarzschild black hole solution. [ABSTRACT FROM AUTHOR]

We present the manifestly covariant canonical operator formalism of a Weyl invariant (or equivalently, a locally scale invariant) gravity whose classical action consists of the well-known conformal gravity and Weyl invariant scalar-tensor gravity, on the basis of the Becchi-Rouet-Stora-Tyupin (BRST) formalism. It is shown that there exists a Poincaré-like IOSp(8|8) global symmetry as in Einstein’s general relativity, which should be contrasted to the case of only the Weyl invariant scalar-tensor gravity where we have a more extended Poincaré-like IOSp(10|10) global symmetry. This reduction of the global symmetry is attributed to the presence of the Stückelberg symmetry. [ABSTRACT FROM AUTHOR]

We provide a formulation of quantum mechanics based on the cohomology of the Batalin-Vilkovisky (BV) algebra. Focusing on quantum-mechanical systems without gauge symmetry we introduce a homotopy retract from the chain complex of the harmonic oscillator to finite-dimensional phase space. This induces a homotopy transfer from the BV algebra to the algebra of functions on phase space. Quantum expectation values for a given operator or functional are computed by the function whose pullback gives a functional in the same cohomology class. This statement is proved in perturbation theory by relating the perturbation lemma to Wick’s theorem. We test this method by computing two-point functions for the harmonic oscillator for position eigenstates and coherent states. Finally, we derive the Unruh effect, illustrating that these methods are applicable to quantum field theory. [ABSTRACT FROM AUTHOR]

In this work we present a complete three-loop renormalisation of an abelian chiral gauge theory within the Breitenlohner-Maison/’t Hooft-Veltman (BMHV) scheme of dimensional regularisation (DReg). In this scheme the γ5-matrix appearing in gauge interactions is a non-anticommuting object, leading to a breaking of gauge and BRST invariance. Employing an efficient method based on the quantum action principle, we obtain the complete three-loop counterterm action which serves both to render the theory finite and to restore gauge and BRST invariance. The UV singular counterterms involve not only higher order ϵ-poles but also new counterterm structures emerging at the three-loop level for the first time; the finite symmetry-restoring counterterms are restricted to the same structures as at lower loop orders, just with different coefficients, aligning with our expectations. Both the singular and the finite counterterms include structures which cannot be obtained by the standard multiplicative renormalisation. Our results demonstrate that a rigorous treatment of chiral gauge theories with γ5 defined in the BMHV scheme at the multi-loop level is possible and that the obtained counterterm action is suitable for computer implementations, allowing automated calculations without ambiguities caused by γ5. [ABSTRACT FROM AUTHOR]

Abstract We propose a procedure of computing the n-point function in perturbation theory of the quantum field theory as the average over the complex Gaussian noises in a classical theory. The complex Gaussian noises are the sources for the creation and annihilation of particles and the energy of the resultant configuration is the same as the zero point energy of the corresponding quantum field theory.

Abstract We study the natural norm on the space of solutions to the Wheeler-DeWitt equation in an asymptotically de Sitter spacetime. We propose that the norm is obtained by integrating the squared wavefunctional over field configurations and dividing by the volume of the diff-and-Weyl group. We impose appropriate gauge conditions to fix the diff- and-Weyl redundancy and obtain a finite expression for the norm using the Faddeev-Popov procedure. This leads to a ghost action that has zero modes corresponding to a residual conformal subgroup of the diff-and-Weyl group. By keeping track of these zero modes, we show that Higuchi’s norm for group-averaged states emerges from our prescription in the nongravitational limit. We apply our formalism to cosmological correlators and propose that they should be understood as gauge-fixed observables. We identify the symmetries of these observables. In a nongravitational theory, it is necessary to specify such correlators everywhere on a Cauchy slice to identify a state in the Hilbert space. In a theory of quantum gravity, we demonstrate a version of the principle of holography of information: cosmological correlators in an arbitrarily small region suffice to completely specify the state.

Abstract We propose a covariant technique to excavate physical bosonic string states by entire trajectories rather than individually. The approach is based on Howe duality: the string’s spacetime Lorentz algebra commutes with a certain inductive limit of sp(•), with the Virasoro constraints forming a subalgebra of the Howe dual algebra sp(•). There are then infinitely many simple trajectories of states, which are lowest-weight representations of sp(•) and hence of the Virasoro algebra. Deeper trajectories are recurrences of the simple ones and can be probed by suitable trajectory-shifting operators built out of the Howe dual algebra generators. We illustrate the formalism with a number of subleading trajectories and compute a sample of tree-level amplitudes.

Abstract We investigate off-shell perturbative renormalisation of pure quantum gravity for both background metric and quantum fluctuations. We show that at each new loop order, the divergences that do not vanish on-shell are constructed from only the total metric, whilst those that vanish on-shell are renormalised by canonical transformations involving the quantum fields. Purely background metric divergences do not separately appear, and the background metric does not get renormalised. We highlight that renormalisation group identities play a crucial rôle ensuring consistency in the renormalisation of BRST transformations beyond one loop order. We verify these assertions by computing leading off- shell divergences to two loops, exploiting off-shell BRST invariance and the renormalisation group equations. Although some divergences can be absorbed by field redefinitions, we explain why this does not lead to finite beta-functions for the corresponding field.

We study the natural norm on the space of solutions to the Wheeler-DeWitt equation in an asymptotically de Sitter spacetime. We propose that the norm is obtained by integrating the squared wavefunctional over field configurations and dividing by the volume of the diff-and-Weyl group. We impose appropriate gauge conditions to fix the diff- and-Weyl redundancy and obtain a finite expression for the norm using the Faddeev-Popov procedure. This leads to a ghost action that has zero modes corresponding to a residual conformal subgroup of the diff-and-Weyl group. By keeping track of these zero modes, we show that Higuchi's norm for group-averaged states emerges from our prescription in the nongravitational limit. We apply our formalism to cosmological correlators and propose that they should be understood as gauge-fixed observables. We identify the symmetries of these observables. In a nongravitational theory, it is necessary to specify such correlators everywhere on a Cauchy slice to identify a state in the Hilbert space. In a theory of quantum gravity, we demonstrate a version of the principle of holography of information: cosmological correlators in an arbitrarily small region suffice to completely specify the state. [ABSTRACT FROM AUTHOR]

We propose a covariant technique to excavate physical bosonic string states by entire trajectories rather than individually. The approach is based on Howe duality: the string's spacetime Lorentz algebra commutes with a certain inductive limit of sp(•), with the Virasoro constraints forming a subalgebra of the Howe dual algebra sp(•). There are then infinitely many simple trajectories of states, which are lowest-weight representations of sp(•) and hence of the Virasoro algebra. Deeper trajectories are recurrences of the simple ones and can be probed by suitable trajectory-shifting operators built out of the Howe dual algebra generators. We illustrate the formalism with a number of subleading trajectories and compute a sample of tree-level amplitudes. [ABSTRACT FROM AUTHOR]

We investigate off-shell perturbative renormalisation of pure quantum gravity for both background metric and quantum fluctuations. We show that at each new loop order, the divergences that do not vanish on-shell are constructed from only the total metric, whilst those that vanish on-shell are renormalised by canonical transformations involving the quantum fields. Purely background metric divergences do not separately appear, and the background metric does not get renormalised. We highlight that renormalisation group identities play a crucial rôle ensuring consistency in the renormalisation of BRST transformations beyond one loop order. We verify these assertions by computing leading off- shell divergences to two loops, exploiting off-shell BRST invariance and the renormalisation group equations. Although some divergences can be absorbed by field redefinitions, we explain why this does not lead to finite beta-functions for the corresponding field. [ABSTRACT FROM AUTHOR]

Abstract The homotopy algebraic formalism of braided noncommutative field theory is used to define the explicit example of braided electrodynamics, that is, U(1) gauge theory minimally coupled to a Dirac fermion. We construct the braided L ∞ -algebra of this field theory and obtain the braided equations of motion, action functional and conserved matter current. The modifications of the electric charge conservation law due to the braided noncommutative deformation are described. We develop a braided generalization of Wick’s theorem, and use it to compute correlation functions of the braided quantum field theory using homological perturbation theory. Our putative calculations indicate that the braided theory does not contain the non-planar Feynman diagrams of conventional noncommutative quantum field theory, and that correlators do not exhibit UV/IR mixing.

Abstract For unimodular gravity, we work out, by using dimensional regularization, the complete one-loop correction to the graviton propagator in any space-time dimension. The computation is carried out within the framework where unimodular gravity has Weyl invariance in addition to the transverse diffeomorphism gauge symmetry. Thus, no Lagrange multiplier is introduced to enforce the unimodularity condition. The quantization of the theory is carried out by using the BRST framework and there considering a large continuous family of gauge-fixing terms. The BRST formalism is developed in such a way that the set of ghost, anti-ghost and auxiliary fields and their BRST changes do not depend on the space-time dimension, as befits dimensional regularization. As an application of our general result, and at D = 4, we obtain the renormalized one-loop graviton propagator in the dimensional regularization minimal subtraction scheme. We do so by considering two simplifying gauge-fixing choices.

Abstract We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the “Operatope”). We derive a set of quadratic recursion relations which appear to fully determine the final answer. Our strategy can be applied to a very general class of twisted supersymmetric quantum field theories.

Abstract The BRST structure of the extended Bondi-Metzner-Sachs symmetry group of asymptotically flat manifolds is investigated using the recently introduced framework of the Beltrami field parametrization of four-dimensional metrics. The latter identifies geometrically the two physical degrees of freedom of the graviton as fundamental fields. The graded BRST BMS4 nilpotent differential operator relies on four horizontality conditions giving a Lagrangian reformulation of the asymptotic BMS4 symmetry. A series of cocycles is found which indicate the possibility of anomalies for three-dimensional Lagrangian theories to be built in the null boundaries of asymptotically flat spaces from the principle of BRST BMS4 invariance.

Abstract Application of the supersymmetric localization method to theories on anti-de Sitter spacetime has received recent interest, yet still remains as a challenging problem. In this paper, we focus on (global) Euclidean AdS2, on which we consider an Abelian 𝒩 = (2, 2) theory and implement localization computation to obtain the exact partition function. For comparison, we also revisit the theory on S2 and perform a parallel computation. We refine the notion of equivariant supersymmetry and use appropriate functional integration measure. For AdS2 we choose a supersymmetric boundary condition which is compatible with the principle of variation. To evaluate the 1-loop determinant about the localization saddle, we use index theory and fixed point formula, where we pay attention to the effect of zero modes and their superpartners. The existence of fermionic superpartner of 1-form boundary zero modes is proven. Obtaining the 1-loop determinant requires expansion of the index that presents an ambiguity, which we resolve using boundary condition. The resulting partition function reveals an overall dependence on the size of the background manifold, AdS2 as well as S2, as a sum of two types of contributions: a local one from local conformal anomaly through the index computation and a global one coming from zero modes. This overall size dependence matches with the perturbative 1-loop evaluation using heat kernel method.

The homotopy algebraic formalism of braided noncommutative field theory is used to define the explicit example of braided electrodynamics, that is, U(1) gauge theory minimally coupled to a Dirac fermion. We construct the braided L∞-algebra of this field theory and obtain the braided equations of motion, action functional and conserved matter current. The modifications of the electric charge conservation law due to the braided noncommutative deformation are described. We develop a braided generalization of Wick's theorem, and use it to compute correlation functions of the braided quantum field theory using homological perturbation theory. Our putative calculations indicate that the braided theory does not contain the non-planar Feynman diagrams of conventional noncommutative quantum field theory, and that correlators do not exhibit UV/IR mixing. [ABSTRACT FROM AUTHOR]

For unimodular gravity, we work out, by using dimensional regularization, the complete one-loop correction to the graviton propagator in any space-time dimension. The computation is carried out within the framework where unimodular gravity has Weyl invariance in addition to the transverse diffeomorphism gauge symmetry. Thus, no Lagrange multiplier is introduced to enforce the unimodularity condition. The quantization of the theory is carried out by using the BRST framework and there considering a large continuous family of gauge-fixing terms. The BRST formalism is developed in such a way that the set of ghost, anti-ghost and auxiliary fields and their BRST changes do not depend on the space-time dimension, as befits dimensional regularization. As an application of our general result, and at D = 4, we obtain the renormalized one-loop graviton propagator in the dimensional regularization minimal subtraction scheme. We do so by considering two simplifying gauge-fixing choices. [ABSTRACT FROM AUTHOR]

Abstract We discuss how renormalisation group equations can be consistently formulated using the algebraic renormalisation framework, in the context of a dimensionally-renormalised chiral field theory in the BMHV scheme, where the BRST symmetry, originally broken at the quantum level, is restored via finite counterterms. We compare it with the more standard multiplicative renormalisation approach, which application would be more cumbersome in this setting. Both procedures are applied and compared on the example of a massless chiral right-handed QED model, and beta-function and anomalous dimensions are evaluated up to two-loop orders.

Abstract We provide an alternative compact expression for the 11D pure spinor b-ghost by introducing a new set of negative ghost number operators made out of non-minimal pure spinor variables. Using the algebraic properties satisfied by these operators, it will be straightforwardly shown that Q b = P 2 2 $$ \left\{Q,b\right\}=\frac{P^2}{2} $$ , as well as {b, b} = QΩ. As an application of this novel formulation, the ghost number two vertex operator will easily be obtained in a completely covariant manner from a standard descent relation, the ghost number three vertex operator will be shown to satisfy the generalized Siegel gauge condition, and the 11D supergravity two-particle superfield will be constructed in a quite simple way.

The BRST structure of the extended Bondi-Metzner-Sachs symmetry group of asymptotically flat manifolds is investigated using the recently introduced framework of the Beltrami field parametrization of four-dimensional metrics. The latter identifies geometrically the two physical degrees of freedom of the graviton as fundamental fields. The graded BRST BMS4 nilpotent differential operator relies on four horizontality conditions giving a Lagrangian reformulation of the asymptotic BMS4 symmetry. A series of cocycles is found which indicate the possibility of anomalies for three-dimensional Lagrangian theories to be built in the null boundaries of asymptotically flat spaces from the principle of BRST BMS4 invariance. [ABSTRACT FROM AUTHOR]

We study a class of universal Feynman integrals which appear in four-dimensional holomorphic theories. We recast the integrals as the Fourier transform of a certain polytope in the space of loop momenta (a.k.a. the "Operatope"). We derive a set of quadratic recursion relations which appear to fully determine the final answer. Our strategy can be applied to a very general class of twisted supersymmetric quantum field theories. [ABSTRACT FROM AUTHOR]

Application of the supersymmetric localization method to theories on anti-de Sitter spacetime has received recent interest, yet still remains as a challenging problem. In this paper, we focus on (global) Euclidean AdS2, on which we consider an Abelian 풩 = (2) theory and implement localization computation to obtain the exact partition function. For comparison, we also revisit the theory on S2 and perform a parallel computation. We refine the notion of equivariant supersymmetry and use appropriate functional integration measure. For AdS2 we choose a supersymmetric boundary condition which is compatible with the principle of variation. To evaluate the 1-loop determinant about the localization saddle, we use index theory and fixed point formula, where we pay attention to the effect of zero modes and their superpartners. The existence of fermionic superpartner of 1-form boundary zero modes is proven. Obtaining the 1-loop determinant requires expansion of the index that presents an ambiguity, which we resolve using boundary condition. The resulting partition function reveals an overall dependence on the size of the background manifold, AdS2 as well as S2, as a sum of two types of contributions: a local one from local conformal anomaly through the index computation and a global one coming from zero modes. This overall size dependence matches with the perturbative 1-loop evaluation using heat kernel method. [ABSTRACT FROM AUTHOR]

Application of the supersymmetric localization method to theories on anti-de Sitter spacetime has received recent interest, yet still remains as a challenging problem. In this paper, we focus on (global) Euclidean AdS2, on which we consider an Abelian 풩 = (2) theory and implement localization computation to obtain the exact partition function. For comparison, we also revisit the theory on S2 and perform a parallel computation. We refine the notion of equivariant supersymmetry and use appropriate functional integration measure. For AdS2 we choose a supersymmetric boundary condition which is compatible with the principle of variation. To evaluate the 1-loop determinant about the localization saddle, we use index theory and fixed point formula, where we pay attention to the effect of zero modes and their superpartners. The existence of fermionic superpartner of 1-form boundary zero modes is proven. Obtaining the 1-loop determinant requires expansion of the index that presents an ambiguity, which we resolve using boundary condition. The resulting partition function reveals an overall dependence on the size of the background manifold, AdS2 as well as S2, as a sum of two types of contributions: a local one from local conformal anomaly through the index computation and a global one coming from zero modes. This overall size dependence matches with the perturbative 1-loop evaluation using heat kernel method. [ABSTRACT FROM AUTHOR]

Abstract Motivated by the results of Anastasiou et al., we consider the convolutional double copy for BRST and anti-BRST covariant formulations of gravitational and gauge theories in more detail. We give a general BRST and anti-BRST invariant formulation of linearised N $$ \mathcal{N} $$ = 0 supergravity using superspace methods and show how this may be obtained from the square of linearised Yang-Mills theories. We demonstrate this relation for the Schwarzschild black hole and the ten-dimensional black string solution as two concrete examples.

Abstract We determine the solution to the classical master equation for a 3D topological field theory with Wess-Zumino term and an underlying geometrical structure of a twisted R-Poisson manifold on its target space. The graded geometry of the target space departs from the usual QP structure encountered in the AKSZ construction of topological sigma models, the obstruction being attributed to the presence of the Wess-Zumino 4-form. Due to the inapplicability of the AKSZ construction in this case, we set up the traditional BV/BRST formalism for twisted R-Poisson sigma models in any dimension, which feature an open gauge algebra and constitute multiple stages reducible constrained Hamiltonian systems. An unusual feature of the theories is that they exhibit non-linear openness of the gauge algebra, in other words products of the equations of motion appear in them. Nevertheless, we find the BV action in presence of the 4-form twist in 3D, namely for a specific 4-form twisted (pre-)Courant sigma model. Moreover, we provide a complete set of explicit formulas for the off-shell nilpotent BV operator for untwisted R-Poisson sigma models in any dimension.

Abstract We propose an analogue of spin fields for the relativistic RNS-particle in 4 dimensions, in order to describe Ramond-Ramond states as “two-particle” excitations on the world line. On a natural representation space we identify a differential whose cohomology agrees with RR-fields equations. We then discuss the non-linear theory encoded in deformations of the latter by background fields. We also formulate a sigma model for this spin field from which we recover the RNS-formulation by imposing suitable constraints.

Abstract There exists a natural L ∞ -algebra or Q-manifold that can be associated to any (gauge) field theory. Perturbatively, it can be obtained by reducing the L ∞ -algebra behind the jet space BV-BRST formulation to its minimal model. We explicitly construct the minimal models of self-dual Yang-Mills and self-dual gravity theories, which also represents their equations of motion as Free Differential Algebras. The minimal model regains all relevant information about the field theory, e.g. actions, charges, anomalies, can be understood in terms of the corresponding Q-cohomology.