arXiv subjects

Alexander Reshetnyak

Publications and source records attributed to Alexander Reshetnyak.

9 recordsLinked to original sources

arXiv2025

Holography and the Swampland: Constraints on Quantum Gravity from Holographic Principles

The Swampland Program aims to delineate the space of consistent low-energy effective field theories (EFTs) that admit a UV completion in quantum gravity from those that do not. In parallel, holography, and particularly the AdS/CFT correspondence, offers a non-perturbative definition of quantum gravity in asymptotically anti-de Sitter (AdS) spacetimes. In this paper, we explore the Swampland Conjectures through the lens of holography, focusing on how holographic consistency conditions, such as the convexity of the conformal field theory (CFT) spectrum, the averaged null energy condition (ANEC), and the modular bootstrap, map onto Swampland constraints in the bulk. We argue that the holographic principle provides a geometric realization of Swampland bounds, particularly on scalar field potentials and the absence of long-lived de Sitter vacua. Finally, we discuss how the emergent bulk locality in AdS/CFT provides evidence that the Swampland conjectures may themselves be manifestations of deeper holographic consistency conditions.

hep-th↗

arXiv2023

BRST-BV approach for interacting higher spin fields

We develop the BRST-BV approach to construct the general off-shell Lorentz covariant cubic, quartic, $e$-tic interaction vertices for irreducible higher spin fields on $d$-dimensional Minkowski space. We consider two different cases for interacting integer higher spin fields both with massless and with massive fields. The deformation procedure to find minimal (determined with help of generalized Hilbert space) BRST-BV action for interacting higher spin fields is based on the preservation of master equation validity in each power of coupling constant $g$ starting from the Lagrangian formulation for free gauge theory. As examples we consider the construction of local cubic vertices for $k$ irreducible massless fields of integer helicities, and $k-1$ massless with one massive fields of spins $s_1, ,..., s_{k-1}, s_k$. For triple of two massless scalars and tensor field of integer spin the BRST-BV action with cubic interaction is explicitly found. Unlike the previous results on cubic vertices we follow our result for BRST approach [arXiv:2105.12030[hep-th]] for massless fields, but for the unique BRST-BV action instead of classical action with reducible gauge transformations. The procedure is based on the complete BRST operator, including the trace constraints that is used to formulate an irreducible representation with definite integer spin.

hep-th↗

arXiv2018

Constrained BRST- BFV Lagrangian formulations for Higher Spin Fields in Minkowski Spaces

BRST-BFV method for constrained Lagrangian formulations (LFs) for (ir)reducible half-integer HS Poincare group representations in Minkowski space is suggested. The procedure is derived by 2 ways: from the unconstrained BRST-BFV method for mixed-symmetry HS fermionic fields subject to an arbitrary Young tableaux with k rows (suggested in arXiv:1211.1273[hep-th]) by extracting the second-class constraints, $\widehat{O}_α=(\widehat{O}_a, \widehat{O}^+_a)$, from a total superalgebra of constraints, second, in self-consistent way by means of finding BRST-extended initial off-shell algebraic constraints, $\widehat{O}_a$. In both cases, the latter constraints supercommute on the constraint surface with constrained BRST $Q_C$ and spin operators $σ^i_C$. The closedness of the superalgebra $Q_C, \widehat{O}_a, σ^i_C$ guarantees that the final gauge-invariant LF is compatible with off-shell constraints $\widehat{O}_a$ imposed on field and gauge parameter vectors of Hilbert space not depending from the ghosts and conversion auxiliary oscillators related to $\widehat{O}_a$, in comparison with vectors for unconstrained BRST-BFV LF. The suggested constrained BRST-BFV approach is valid for both massive HS fields and integer HS fields in the second-order formulation. It is shown that the respective constrained and unconstrained LFs for (half)-integer HS fields with a given spin are equivalent. The constrained Lagrangians in ghost-independent and component (for initial spin-tensor field) are obtained and shown to coincide with Fang-Fronsdal formulation for constrained totally-symmetric HS field. The triplet and unconstrained quartet LFs for the latter field and gauge-invariant constrained Lagrangians for a massive field of spin n+1/2 are derived. A concept of BRST-invariant second-class constraints for a general dynamical system with mixed-class constraints is suggested.

hep-th↗

arXiv2018

Generalization of Faddeev--Popov Rules in Yang--Mills Theories: N=3,4 BRST Symmetries

The Faddeev-Popov rules for quantization of theory with gauge group are generalized for case of nvariance of quantum actions, $S_N$, on N-parametric Abelian SUSY transformations with odd parameters $λ_p$, p=1,..,N and anticommuting generators $s_p$, for N=3,4 implying substitution of ghost fields N-plet, $C^p$ multipled on $λ_p$, instead of the parameter, $ξ$, of gauge transformations. Total configuration spaces for quantum theory of the same classical model coincide for N=3 ,4 cases. For N=3 transformations the superspace of irrep includes in addition 3 ghost $C^p$, 3 even $B^{pq}$ and odd $\hat{B}$ fields for p,q=1-3. It is shown for quantum action $S_{3}$ the gauge-fixing by adding to classical action of N=3-exact term requires 1 antighost $\bar{C}$, 3 even $B^{p}$ 3 odd $\hat{B}{}^p$ and Nakanishi--Lautrup fields. Action of N=3 transformations on the latter fields is found. The transformations appear by N=3 BRST ones for the vacuum functional, $Z_3(0) $. It is shown, the configuration space appears by irrep superspace for fields $Φ_4$ for N=4- transformations containing in addition to $A^μ$: (4+6+4+1) ghost-antighost $C^r$, even $B^{rs}$, odd $\hat{B}{}^r $ fields and B. Action $S_4$ is constructed by adding to classical action of N=4-exact with gauge boson $F_4$ as compared to gauge fermion $Ψ_3$ for N=3 case. Procedure is valid for any admissible gauge. The equivalence with $N=1$ BRST-invariant quantization method is explicitly found. Finite N=3,4 BRST transformations are derived from algebraic transformations. Respective Jacobians for field-dependent parameters are calculated. They imply the presence of corresponding modified Ward identity to be reduced to new (usual) Ward identities for constant parameters and describe the problem of gauge-dependence. Introduction into diagrammatic Feynman techniques for N=3,4 cases is suggested.

hep-th↗

arXiv2016

Comments on interactions in the SUSY models

We consider special supersymmetry (SUSY) transformations with $m$ generators $\overleftarrow{s}_{α}$ for a certain class of models and study some physical consequences of Grassmann-odd transformations which form an Abelian supergroup with finite parameters and respective group-like elements being functionals of field variables. The SUSY-invariant path integral measure within conventional quantization implies the appearance, under a change of variables related to such SUSY transformations, of a Jacobian which is explicitly calculated. The Jacobian implies, first of all, the appearance of trivial interactions in the transformed action, and, second, the presence of a modified Ward identity which reduces to the standard Ward identities in the case of constant parameters. We examine the case of ${N}=1$ and $N=2$ supersymmetric harmonic oscillators to illustrate the general concept by a simple free model with $(1,1)$ physical degrees of freedom. It is shown that the interaction terms $U_{tr}$ have a corresponding SUSY-exact form: $U_{tr}=% \big(V_{(1)}\overleftarrow{s};V_{(2)}\overleftarrow{\bar{s}}\overleftarrow{s}% \big)$ naturally generated in this generalized formulation. We argue that the case of non-trivial interactions cannot be obtained in such a way.

physics.gen-ph↗

arXiv2014

On Gauge Independence for Gauge Models with Soft Breaking of BRST Symmetry

A consistent quantum treatment of general gauge theories with an arbitrary gauge-fixing in the presence of soft breaking of the BRST symmetry in the field-antifield formalism is developed. It is based on a gauged (involving a field-dependent parameter) version of finite BRST transformations. The prescription allows one to restore the gauge-independence of the effective action at its extremals and therefore also that of the conventional $S$-matrix for a theory with BRST-breaking terms being additively introduced into a BRST-invariant action in order to achieve a consistency of the functional integral. We demonstrate the applicability of this prescription within the approach of functional renormalization group to the Yang--Mills and gravity theories. The Gribov--Zwanziger action and the refined Gribov--Zwanziger action for a many-parameter family of gauges, including the Coulomb, axial and covariant gauges, are derived perturbatively on the basis of finite gauged BRST transformations starting from Landau gauge. It is proved that gauge theories with soft breaking of BRST symmetry can be made consistent if the transformed BRST-breaking terms satisfy the same soft BRST symmetry breaking condition in the resulting gauge as the untransformed ones in the initial gauge, and also without this requirement.

hep-th↗

arXiv2013

On the vibron dressing in the $α$--helicoidal macromolecular chains

We present a study of the physical properties of the vibrational excitation in $α$--helicoidal macromolecular chains, caused by the interaction with acoustical and optical phonon modes. The influence of the temperature and the basic system parameters on the vibron dressing has been analyzed by employing the simple mean--field approach based on the variational extension of the Lang--Firsov unitary transformation. Applied approach predicts a region in system parameter space where one takes place an abrupt transition from partially dressed (light and mobile) to fully dressed (immobile) vibron states. We found that the boundary of this region depends on system temperature and type of bond among structural elements in the macromolecular chain.

physics.chem-ph↗

arXiv2011

On representations of Higher Spin symmetry algebras for mixed-symmetry HS fields on AdS-spaces. Lagrangian formulation

We derive non-linear commutator HS symmetry algebra, which encode unitary irreducible representations of AdS group subject to Young tableaux $Y(s_1,...,s_k)$ with $k\geq 2$ rows on $d$-dimensional anti-de-Sitter space. Auxiliary representations for specially deformed non-linear HS symmetry algebra in terms of generalized Verma module in order to additively convert a subsystem of second-class constraints in the HS symmetry algebra into one with first-class constraints are found explicitly for the case of HS fields for $k=2$ Young tableaux. The oscillator realization over Heisenberg algebra for obtained Verma module is constructed. The results generalize the method of auxiliary representations construction for symplectic $sp(2k)$ algebra used for mixed-symmetry HS fields on a flat spaces and can be extended on a case of arbitrary HS fields in AdS-space. Gauge-invariant unconstrained reducible Lagrangian formulation for free bosonic HS fields with generalized spin $(s_1,s_2)$ is derived.

hep-th↗

arXiv2011

Is soft breaking of BRST symmetry consistent?

A definition of soft breaking of BRST symmetry in the field-antifield formalism is proposed, valid for general gauge theories and arbitrary gauge fixing. The Ward identities for the generating functionals of Green's functions are derived, and their gauge dependence is investigated. We discuss the Gribov-Zwanziger action for the one-parameter family of R_xi gauges. It is argued that gauge theories with a soft breaking of BRST symmetry are inconsistent.

hep-th↗