Covariant Effective Action and One-Loop Renormalization of 2D Dilaton Gravity with Fermionic Matter

TL;DR

This paper derives the one-loop covariant effective action for 2D dilaton gravity coupled with fermionic matter, addressing technical challenges and establishing conditions for renormalizability, thus advancing quantum gravity models in two dimensions.

Contribution

It provides the first comprehensive derivation of the one-loop effective action for 2D dilaton gravity with fermions, including Majorana and Dirac spinors, and discusses renormalization conditions.

Findings

Effective action for Majorana spinors obtained

Conditions for multiplicative renormalizability established

Comparison with classical gravitational field conducted

Abstract

Two dimensional dilaton gravity interacting with a four-fermion model and scalars is investigated, all the coefficients of the Lagrangian being arbitrary functions of the dilaton field. The one-loop covariant effective action for 2D dilaton gravity with Majorana spinors (including the four-fermion interaction) is obtained, and the technical problems which appear in an attempt at generalizing such calculations to the case of the most general four-fermion model described by Dirac fermions are discussed. A solution to these problems is found, based on its reduction to the Majorana spinor case. The general covariant effective action for 2D dilaton gravity with the four-fermion model described by Dirac spinors is given. The one-loop renormalization of dilaton gravity with Majorana spinors is carried out and the specific conditions for multiplicative renormalizability are found. A comparison with the same theory but with a classical gravitational field is done.