Quantum Dilaton Gravity in Two Dimensions with Fermionic Matter

TL;DR

This paper performs path integral quantization of two-dimensional dilaton gravity coupled to fermionic matter, deriving gravitational vertices and discussing implications for bosonisation.

Contribution

It provides the first exact integration of geometry in fermionic dilaton gravity and analyzes matter interactions, extending previous scalar matter results.

Findings

Exact geometric integration achieved

Derived lowest order gravitational vertices for fermionic matter

Discussed relevance for bosonisation and matter interactions

Abstract

Path integral quantization of generic two-dimensional dilaton gravity non-minimally coupled to a Dirac fermion is performed. After integrating out geometry exactly, perturbation theory is employed in the matter sector to derive the lowest order gravitational vertices. Consistency with the case of scalar matter is found and issues of relevance for bosonisation are pointed out.