Induced Chiral Supergravities in 2D

TL;DR

This paper investigates the induced actions of 2D supergravities from chiral conformal supermatter, highlighting anomalies and their super-reparametrization invariant formulations, with applications to string theories.

Contribution

It derives super-reparametrization invariant induced actions for 2D supergravities with anomalies, extending understanding of their quantization and relation to string models.

Findings

Induced actions exhibit super-Weyl and super-Lorentz anomalies.

Actions can be defined invariant under super-reparametrization despite anomalies.

Connections established between these actions and chiral super-Liouville theory in string contexts.

Abstract

We analyze actions for 2D supergravities induced by chiral conformal supermatter. The latter may be thought as described at the classical level by superspace actions invariant under super-reparametrization, super-Weyl and super-Lorentz transformations. Upon quantization various anomalies appear which characterize the non-trivial induced actions for the supergravitational sector. We derive these induced actions using a chiral boson to represent the chiral inducing matter. We show that they can be defined in a super-reparametrization invariant way, but with super-Weyl and super-Lorentz anomalies. We consider the case of $(1,0)$ and $(1,1)$ supergravities by working in their respective superspace formulations and investigate their quantization in the conformal gauge. The actions we consider arise naturally in off-critical heterotic and spinning strings. In the conformal gauge, they correspond to chiral extensions of the super-Liouville theory.