Observations on the Topological Structure in 2d Gravity Coupled to Minimal Matter

TL;DR

This paper reveals the topological gravity structure in 2D gravity coupled with minimal matter models using bosonization, connecting cohomology classes and ground ring generators in string theory.

Contribution

It uncovers the topological gravity structure in 2D gravity with minimal models and relates cohomology classes to string theory ground ring generators.

Findings

Topological gravity structure identified in 2D gravity with minimal matter.

Cohomology class of fermionic charge is isomorphic to the BRST charge.

Ground ring generator found in equivariant cohomology.

Abstract

By using a bosonization we uncover the topological gravity structure of Labastida, Pernici and Witten in ordinary $2d$ gravity coupled to $(p,q)$ minimal models. We study the cohomology class associated with the fermionic charge of the topological gravity which is shown to be isomorphic to that of the total $BRST$ charge. One of the ground ring generators of $c_M <1$ string theory is found to be in the equivariant cohomology of this fermionic charge.