N=2 Supersymmetry in Two-Dimensional Dilaton Gravity

TL;DR

This paper develops an $N=2$ supersymmetric extension of two-dimensional dilaton gravity, analyzing its renormalization properties and identifying which terms are protected by supersymmetry in a superconformal gauge.

Contribution

It constructs the most general $N=2$ supersymmetric dilaton gravity action in two dimensions and studies its renormalization behavior, highlighting the role of chiral terms.

Findings

Most general $N=2$ supersymmetric action includes chiral terms.

One chiral term becomes nonchiral in superconformal gauge.

Only one term remains protected from renormalization.

Abstract

Actions for $D=2$, $N=2$ supergravity coupled to a scalar field are calculated, and it is shown that the most general power-counting renormalizable dilaton gravity action has an $N=2$ locally supersymmetric extension. The presence of chiral terms in the action leads one to hope that non-renormalization theorems similar to those in global SUSY will apply; this would eliminate some of the renormalization ambiguities which plague ordinary bosonic (and $N=1$) dilaton gravity. To investigate this, the model is studied in superconformal gauge, where it is found that one chiral term becomes nonchiral, so that only one term is safe from renormalization.