Topological Gravity with Non-Compact Matter

TL;DR

This paper develops a framework for topological gravity coupled with non-compact matter models, deriving correlation functions, recursion relations, and critical exponents, and explores implications for two-dimensional gravity beyond the N=2 barrier.

Contribution

It introduces a novel approach to coupling non-compact N=(2,2) models with topological gravity and derives new recursion relations and critical exponents.

Findings

Correlation functions based on KP hierarchy

Recursion relations for all genera

Critical exponents computed

Abstract

We couple twisted non-compact N=(2,2) supersymmetric models to topological gravity in two dimensions. We propose expressions for the genus zero correlation functions based on a Kadomtsev-Petviashvili integrable hierarchy. Moreover, we prove recursion relations satisfied by the topological gravity amplitudes at all genera and compute characteristic critical exponents. We discuss the extent to which moving beyond the N=2 central charge barrier opens a window on two-dimensional gravity with central charge larger than one.