Workshop, Maxim Grigoriev: Background fields and (super)symmetries in the presymplectic BV-AKSZ  approach.

Speaker
Maxim Grigoriev, Mons University

Abstract
The presymplectic  BV-AKSZ approach  allows to encode the BV formulation of a local gauge theory into the finite-dimensional graded-geometrical object and can be thought of as an extension of AKSZ construction to the case of generic local theories. After a brief review of the approach, the presymplectic BV-AKSZ formulation for N=1 supergravity in 4 dimensions is presented and shown to give a concise description of the BV formulation. It turns out that the presymplectic BV-AKSZ approach and its nonlagrangian version admit  a natural extension which incorporates theories coupled to background geometries and the corresponding symmetries.  Moreover, (presymplectic) AKSZ models, at least at the level of equations of motion, can be equivalently reformulated in the spacetimes obtained by adding or eliminating contractible dimensions. These can be applied to systematically relate the spacetime and the superspace formulations of supersymmetric systems. As an illustration the toy model of the supersymmetric particle is considered.