Effective gravitational action for 2D massive fermions

TL;DR

This paper derives the effective gravitational action for two-dimensional massive fermions, revealing contributions from Liouville and Mabuchi actions along with non-local terms, in a small mass expansion.

Contribution

It extends the understanding of 2D massive fermions by explicitly computing the gravitational action including non-local terms and Mabuchi contributions.

Findings

Effective action includes Liouville and Mabuchi terms.

Non-local Green's function contributions are identified.

Results generalize previous scalar field findings to fermions.

Abstract

We work out the effective gravitational action for 2D massive Euclidean fermions in a small mass expansion. Besides the leading Liouville action, the order $m^2$ gravitational action contains a piece characteristic of the Mabuchi action, much as for 2D massive scalars, but also several non-local terms involving the Green's functions and Green's functions at coinciding points on the manifold.