Superfield BRST Charge and the Master Action

TL;DR

The paper addresses unifying Hamiltonian BRST (BFV) quantization and Lagrangian BV quantization via a superfield formulation in extended phase space. By introducing an odd coordinate $\theta$ and a superfield BRST data $Q=\Omega+\theta H$, it shows that the BV master action naturally emerges from BFV data and that the master equation $(S,S)=0$ follows from a nilpotent BRST charge. It further provides an inverse construction demonstrating a dual phase-space description where a BV master action $S$ determines a BRST charge $\Omega$ through a $\theta$-integration, revealing a phase-space/Lagrangian duality and enriching the interpretation of ghosts and reducibility. Geometrically, the AKSZ framework on super path spaces unifies even and odd bracket structures, recovering known master actions (e.g., Chern–Simons, Poisson sigma model) and connecting BFV, BV, and AKSZ into a single coherent picture that encompasses Kontsevich's star product context.

Abstract

Using a superfield formulation of extended phase space, we propose a new form of the Hamiltonian action functional. A remarkable feature of this construction is that it directly leads to the BV master action on phase space. Conversely, superspace can be used to construct nilpotent BRST charges directly from solutions to the classical Lagrangian Master Equation. We comment on the relation between these constructions and the specific master action proposal of Alexandrov, Kontsevich, Schwarz and Zaboronsky.