Quantum Field Theory as Effective BV Theory from Chern-Simons

TL;DR

This paper develops a method to compute cohomologies of the BV operator in Chern-Simons-like theories, demonstrating its application to both classical gauge models and AKSZ formulations, revealing insights into their effective actions.

Contribution

It introduces a procedure for explicit cohomology calculations of the BV operator in Chern-Simons and related theories, connecting classical and AKSZ formulations.

Findings

Reproduces BV effective action for a 2D gauge model with matter fields.

Shows the method's applicability to both singular and regular points in the theory space.

Establishes a link between classical Chern-Simons-like theories and AKSZ BF theories.

Abstract

The general procedure for obtaining explicit expressions for all cohomologies of N.Berkovits's operator is suggested. It is demonstrated that calculation of BV integral for the classical Chern-Simons-like theory (Witten's OSFT-like theory) reproduces BV version of two dimensional gauge model at the level of effective action. This model contains gauge field, scalars, fermions and some other fields. We prove that this model is an example of "singular" point from the perspective of the suggested method for cohomology evaluation. For arbitrary "regular" point the same technique results in AKSZ(Alexandrov, Kontsevich, Schwarz, Zaboronsky) version of Chern-Simons theory (BF theory) in accord with [2,3].