ON GRAVITATIONAL DRESSING OF 2D FIELD THEORIES IN CHIRAL GAUGE

TL;DR

This paper explores how matter correlation functions in 2D chiral gauge theories are affected by gravity, revealing that gravitational dressing can eliminate explicit factors and induce non-perturbative logarithmic singularities.

Contribution

It provides a detailed analysis of gravitational dressing in 2D chiral gauge theories, including an exact solution of Ward identities and insights into operator product expansions.

Findings

Gravitational dressing can remove explicit dressing factors in chiral gauge

Four-point functions exhibit logarithmic singularities due to gravity

Perturbative evidence suggests possible integrability of the model with gravity

Abstract

After giving a pedagogical review of the chiral gauge approach to 2D gravity, with particular emphasis on the derivation of the gravitational Ward identities, we discuss in some detail the interpretation of matter correlation functions coupled to gravity in chiral gauge. We argue that in chiral gauge no {\it explicit} gravitational dressing factor, analogue to the Liouville exponential in conformal gauge, is necessary for left-right symmetric matter operators. In particular, we examine the gravitationally dressed four-point correlation function of products of left and right fermions. We solve the corresponding gravitational Ward identity exactly: in the presence of gravity this four-point function exhibits a logarithmic short-distance singularity, instead of the power-law singularity in the absence of gravity. This rather surprising effect is non-perturbative in the gravitational coupling and is a sign for logarithms in the gravitationally dressed operator product expansions. We also discuss some perturbative evidence that the chiral Gross-Neveu model may remain integrable when coupled to gravity.