Non-minimal couplings in two dimensional gravity: a quantum investigation

TL;DR

This paper explores quantum effects of non-minimal matter-gravity couplings in a two-dimensional fermionic model, revealing new interactions, quantization rules, and an alternative gravitational action that could relate to minimal conformal series.

Contribution

It provides the first detailed quantum analysis of non-minimal couplings in 2D gravity, deriving explicit correlation functions and an innovative effective gravitational action.

Findings

Quantization rules for coupling constants derived

Explicit two-point and chiral condensate functions computed

A new non-local effective gravitational action identified

Abstract

We investigate the quantum effects of the non-minimal matter-gravity couplings derived by Cangemi and Jackiw in the realm of a specific fermionic theory, namely the abelian Thirring model on a Riemann surface of genus zero and one. The structure and the strength of the new interactions are seen to be highly constrained, when the topology of the underlying manifold is taken into account. As a matter of fact, by requiring to have a well-defined action, we are led both to quantization rules for the coupling constants and to selection rules for the correlation functions. Explicit quantum computations are carried out in genus one (torus). In particular the two-point function and the chiral condensate are carefully derived for this case. Finally the effective gravitational action, coming from integrating out the fermionic degrees of freedoom, is presented. It is different from the standard Liouville one: a new non-local functional of the conformal factor arises and the central charge is improved, depending also on the Thirring coupling constant. This last feature opens the possibility of giving a new explicit representation of the minimal series in terms of a fermionic interacting model.