Constrained Topological Field Theory

TL;DR

This paper develops a formalism for constrained topological gravity derived from N=2 Liouville theory, providing insights into the moduli space constraint and a framework for future research.

Contribution

It introduces a new formalism to handle global and local degrees of freedom in constrained topological gravity, clarifying the origin of the moduli space constraint.

Findings

The moduli space constraint emerges naturally from gauge-fixing.

A formalism for treating degrees of freedom in constrained topological gravity is established.

Provides a basis for future studies on matter coupling and holomorphic anomaly effects.

Abstract

We derive a model of constrained topological gravity, a theory recently introduced by us through the twist of N=2 Liouville theory, starting from the general BRST algebra and imposing the moduli space constraint as a gauge fixing. To do this, it is necessary to introduce a formalism that allows a careful treatment of the global and the local degrees of freedom of the fields. Surprisingly, the moduli space constraint arises from the simplest and most natural gauge-fermion ({\sl antighost} $\times$ {\sl Lagrange multiplier}), confirming the previous results. The simplified technical set-up provides a deeper understanding for constrained topological gravity and a convenient framework for future investigations, like the matter coupling and the analysis of the effects of the constraint on the holomorphic anomaly.