2d, N=2 and N=4 supergravity and the Liouville theory in superspace

TL;DR

This paper constructs manifestly supersymmetric actions for N=2 and N=4 super-Liouville theories coupled to conformal supergravity in superspace, revealing the multiplet structure and kinetic terms via WZNW models.

Contribution

It provides the first explicit superspace formulations of N=2 and N=4 super-Liouville theories coupled to supergravity, identifying the supermultiplets and their kinetic terms.

Findings

N=2 and N=4 super-Liouville actions constructed in superspace.

Identification of the supermultiplets as twisted-II scalar multiplet TM-II.

Kinetic terms described by SU(2)xU(1) WZNW model.

Abstract

The two-dimensional manifestly locally supersymmetric actions describing the N=2 and N=4 extended super-Liouville theory coupled to the N=2 and N=4 conformal supergravity, respectively, are constructed in superspace. It is shown that the N=4 super-Liouville multiplet is described by the improved twisted-II scalar multiplet TM-II, whose kinetic terms are given by the SU(2)xU(1) WZNW model.