Related papers: Classical BV theories on manifolds with boundary
The Batalin-Vilkovisky formulation of a general local gauge theory can be encoded in the structure of a so-called presymplectic gauge PDE -- an almost-$Q$ bundle over the spacetime exterior algebra, equipped with a compatible presymplectic…
Manifolds with boundary, with corners, $b$-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as $E$-manifolds. $E$-manifolds were introduced in [NT01] and investigated in depth…
We compute the extension of the BV theory for three-dimensional General Relativity to all higher-codimension strata - boundaries, corners and vertices - in the BV-BFV framework. Moreover, we show that such extension is strongly equivalent…
A geometric multisymplectic formulation of the classical BRST symmetry of constrained first-order classical field theories is described. To effect this we introduce graded analogues of the bundles and manifolds of the multisymplectic…
We study PL bordism theories from a quantitative perspective. Such theories include those of PL manifolds, ordinary homology theory, as well as various more exotic theories such as bordism of Witt spaces. In all these cases we show that a…
We draw a parallel between the BV/BRST formalism for higher-dimensional ($\ge 2$) Hamiltonian mechanics and higher notions of torsion and basic curvature tensors for generalized connections in specific Lie $n$-algebroids based on homotopy…
Static manifolds with boundary were recently introduced by Cruz and Vit\'orio in the context of the prescribed scalar curvature problem in a manifold with boundary with prescribed mean curvature. This kind of manifold is also interesting…
We define a family of observables for abelian Yang-Mills fields associated to compact regions $U \subseteq M$ with smooth boundary in Riemannian manifolds. Each observable is parametrized by a first variation of solutions and arises as the…
In three dimensional spacetime with negative cosmology constant, the general relativity can be written as two copies of SO$(2,1)$ Chern-Simons theory. On a manifold with boundary the Chern-Simons theory induces a conformal field theory--WZW…
The BFV-formalism was introduced to handle classical systems, equipped with symmetries. It associates a differential graded Poisson algebra to any coisotropic submanifold $S$ of a Poisson manifold $(M,\Pi)$. However the assignment…
We consider a class of \textit{factorizable} Poisson brackets which includes almost all reasonable Poisson structures. A particular case of the factorizable brackets are those associated with symplectic Lie algebroids. The BRST theory is…
It is shown by Connes, Douglas and Schwarz that gauge theory on noncommutative torus describes compactifications of M-theory to tori with constant background three-form field. This indicates that noncommutative gauge theories on more…
We consider a generic gauge system, whose physical degrees of freedom are obtained by restriction on a constraint surface followed by factorization with respect to the action of gauge transformations; in so doing, no Hamiltonian structure…
We study field theories defined in regions of the spatial non-commutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half plane. We find that classical…
We propose a classical model for the non-Abelian Chern-Simons theory coupled to $N$ point-like sources and quantize the system using the BRST technique. The resulting quantum mechanics provides a unified framework for fractional spin, braid…
We apply the intertwiner operator method of arXiv:2411.08865 to topological field theories, including BF theories, Chern-Simons theory, and three-dimensional gravity. We construct the operator on foliated manifolds while preserving…
A general field-antifield BV formalism for antisymplectic first class constraints is proposed. It is as general as the corresponding symplectic BFV-BRST formulation and it is demonstrated to be consistent with a previously proposed…
GSO projected Superconformal field theory (Spin Model) with boundary is considered. There were written the boundary states. For this model were derived one-point structure constants and "bootstrap" equations for boundary-bulk structure…
We present a concise method to construct a BRST invariant action for the topological quantum field theories in the Batalin-Vilkovisky antifield formalism. The BV action that is a solution for the master equation is directly obtained by…
We discuss some basic aspects of quantum fields on star graphs, focusing on boundary conditions, symmetries and scale invariance in particular. We investigate the four-fermion bulk interaction in detail. Using bosonization and vertex…