The Batalin-Vilkovisky Formalism on Fermionic Kaehler Manifolds

TL;DR

This paper integrates fermionic Kähler geometry into the Batalin-Vilkovisky formalism, constructing a fermionic Kähler phase space and providing solutions to the master equation.

Contribution

It introduces a natural incorporation of Kähler structures into the BV formalism, explicitly constructing fermionic irreducible hermitian symmetric spaces.

Findings

Phase space becomes a fermionic Kähler manifold

Explicit construction of fermionic irreducible hermitian symmetric space

Provides solutions to the BV master equation

Abstract

We show that the Kaehler structure can be naturally incorporated in the Batalin-Vilkovisky formalism. The phase space of the BV formalism becomes a fermionic Kaehler manifold. By introducing an isometry we explicitly construct the fermionic irreducible hermitian symmetric space. We then give some solutions of the master equation in the BV formalism.