Related papers: Consistent deformations in the presymplectic BV-AK…
In this paper we will analyse a three dimensional super-Yang-Mills theory on a deformed superspace with boundaries. We show that it is possible to obtain an undeformed theory on the boundary if the bulk superspace is deformed by imposing a…
Slender beams are often employed as constituents in engineering materials and structures. Prior experiments on lattices of slender beams have highlighted their complex failure response, where the interplay between buckling and fracture…
We consider a general reducible gauge theory deformed by mass or/and interaction terms violating gauge invariance. It is shown that in the Abelian case, by using the Stueckelberg-type procedure, this theory with broken gauge symmetry can be…
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…
Subject of this work is a class of Chern-Simons field theories with non-semisimple gauge group, which may well be considered as the most straightforward generalization of an Abelian Chern-Simons field theory. As a matter of fact these…
The local BRST cohomology of the gauged non-linear sigma model on a group manifold is worked out for any Lie group G. We consider both, the case where the gauge field is dynamical and the case where it has no kinetic term (G/G topological…
We propose a new mechanism for formation of topological defects in a U(1) model with a local gauge symmetry. This mechanism leads to definite predictions, which are qualitatively different from those of the Kibble-Zurek mechanism of global…
We extend the author's and CPTVV's correspondence between shifted symplectic and Poisson structures to establish a correspondence between exact shifted symplectic structures and non-degenerate shifted Poisson structures with formal…
We reformulate and motivate AKSZ-type topological field theories in pedestrian terms, explaining how they arise as the most general Schwartz-type topological actions subject to a simple constraint, and how they generalize Chern$-$Simons…
Chern-Simons gauge theory, since its inception as a topological quantum field theory, has proved to be a rich source of understanding for knot invariants. In this work the theory is used to explore the definition of the expectation value of…
We describe constructing solutions of the field equations of Chern-Simons and topological BF theories in terms of deformation theory of locally constant (flat) bundles. Maps of flat connections into one another (dressing transformations)…
The purpose of this paper is to study local cohomology in the noncommutative algebraic geometry framework of Artin and Zhang. The noncommutative spaces are obtained by base change of a Grothendieck category that is locally noetherian or…
We describe a globalization construction for the Rozansky-Witten model in the BV-BFV formalism for a source manifold with and without boundary in the classical and quantum case. After having introduced the necessary background, we define an…
The geometry of supermanifolds provided with $Q$-structure (i.e. with odd vector field $Q$ satisfying $\{ Q,Q\} =0$), $P$-structure (odd symplectic structure ) and $S$-structure (volume element) or with various combinations of these…
We prove an asymptotic product formula for the refined BPS invariants associated with a local del Pezzo surface. Our formula governs the cohomological stabilization of the perverse filtration on the intersection cohomology of the moduli…
The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…
We analyze in detail the equivariant supersymmetry of the $G/G$ model. In spite of the fact that this supersymmetry does not model the infinitesimal action of the group of gauge transformations, localization can be established by standard…
We study gauge theory with finite group $G$ on a graph $X$ using noncommutative differential geometry and Hopf algebra methods with $G$-valued holonomies replaced by gauge fields valued in a `finite group Lie algebra' subset of the group…
We review the results of our research [A.A. Reshetnyak, IJMPA 29 (2014) 1450184; P.Yu. Moshin, A.A. Reshetnyak, Nucl. Phys. B 888 (2014) 92; P.Yu. Moshin, A.A. Reshetnyak, Phys. Lett. B 739 (2014) 110; P.Yu. Moshin, A.A. Reshetnyak,…
We present a perturbative construction of interacting quantum field theories on any smooth globally hyperbolic manifold. We develop a purely local version of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization using…