A Functional and Lagrangian Formulation of Two-Dimensional Topological Gravity

TL;DR

This paper develops a functional and Lagrangian approach to two-dimensional topological gravity, deriving key identities and analyzing gauge independence of correlators within the moduli space framework.

Contribution

It introduces a novel functional and Lagrangian formulation of 2D topological gravity, including derivation of Slavnov-Taylor identities and analysis of gauge invariance.

Findings

Correlators are globally defined forms on moduli space.

Potential gauge dependence linked to the non-trivial line bundle on moduli space.

The first Chern class relates to topological invariants of Mumford, Morita, and Miller.

Abstract

We reconsider two-dimensional topological gravity in a functional and lagrangian framework. We derive its Slavnov-Taylor identities and discuss its (in)dependence on the background gauge. Correlators of reparamerization invariant observables are shown to be globally defined forms on moduli space. The potential obstruction to their gauge-independence is the non-triviality of the line bundle on moduli space ${\cal L}_x$, whose first Chern-class is associated to the topological invariants of Mumford, Morita and Miller. Based on talks given at the Fubini Fest, Torino, 24-26 February 1994, and at the Workshop on String Theory, Trieste, 20-22 April 1994.