Holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity

TL;DR

This paper develops a gauge-invariant action for holomorphic Chern-Simons theory coupled to off-shell Kodaira-Spencer gravity, incorporating complex structure and (3,0)-form backgrounds with BRST and BV formalisms.

Contribution

It introduces a novel off-shell coupling of holomorphic Chern-Simons theory to gravitational backgrounds using an enlarged field space and superfield formalism.

Findings

Constructed a gauge-invariant off-shell action with Lagrange multipliers and ghosts.

Expressed BRST and BV structures in terms of superfields including backgrounds.

Derived a Ward identity linking anti-holomorphic dependence of correlators.

Abstract

We construct an action for holomorphic Chern-Simons theory that couples the gauge field to off-shell gravitational backgrounds, comprising the complex structure and the (3,0)-form of the target space. Gauge invariance of the off-shell action is achieved by enlarging the field space to include an appropriate system of Lagrange multipliers, ghost and ghost-for-ghost fields. Both the BRST transformations and the BV action are compactly and neatly written in terms of superfields which include fields, backgrounds and their antifields. We show that the anti-holomorphic target space derivative can be written as a BRST-commutator on a functional space containing the anti-fields of both the dynamical fields and the gravitational backgrounds. We derive from this result a Ward identity that determines the anti-holomorphic dependence of physical correlators.