The BV action of 3D twisted R-Poisson sigma models

TL;DR

This paper constructs the BV action for 3D twisted R-Poisson sigma models with Wess-Zumino terms, addressing the challenges posed by non-standard graded geometries and open gauge algebras.

Contribution

It develops the BV formalism for twisted R-Poisson sigma models, including explicit formulas and handling non-linear open gauge algebras in any dimension.

Findings

BV action for 3D twisted R-Poisson sigma model with Wess-Zumino term derived

Explicit formulas for off-shell nilpotent BV operator in untwisted models provided

Addressed non-linear openness of gauge algebra in topological field theories

Abstract

We determine the solution to the classical master equation for a 3D topological field theory with Wess-Zumino term and an underlying geometrical structure of a twisted R-Poisson manifold on its target space. The graded geometry of the target space departs from the usual QP structure encountered in the AKSZ construction of topological sigma models, the obstruction being attributed to the presence of the Wess-Zumino 4-form. Due to the inapplicability of the AKSZ construction in this case, we set up the traditional BV/BRST formalism for twisted R-Poisson sigma models in any dimension, which feature an open gauge algebra and constitute multiple stages reducible constrained Hamiltonian systems. An unusual feature of the theories is that it exhibits non-linear openness of the gauge algebra, in other words products of the equations of motion appear in it. Nevertheless, we find the BV action in presence of the 4-form twist in 3D, namely for a specific 4-form twisted (pre-)Courant sigma model. Moreover, we provide a complete set of explicit formulas for the off-shell nilpotent BV operator for untwisted R-Poisson sigma models in any dimension.