(4,4) superfield supergravity

TL;DR

This paper develops a comprehensive framework for (4,4) supergravity in two dimensions using superfield constraints, invariant under super-Weyl transformations, and constructs matter couplings and actions relevant for supersymmetric string theories.

Contribution

It introduces the N=4 superspace constraints for (4,4) supergravity, expresses superfield strengths via twisted multiplets, and constructs invariant matter actions including a superconformal Liouville action.

Findings

Superfield constraints are invariant under super-Weyl transformations.

Explicit matter couplings with spontaneous supersymmetry breaking are constructed.

A superconformally invariant Liouville action for non-critical strings is formulated.

Abstract

We present the N=4 superspace constraints for the two-dimensional (2d) off-shell (4,4) supergravity with the superfield strengths expressed in terms of a (4,4) twisted (scalar) multiplet TM-I, as well as the corresponding component results, in a form suitable for applications. The constraints are shown to be invariant under the N=4 super-Weyl transformations, whose N=4 superfield parameters form another twisted (scalar) multiplet TM-II. To solve the constraints, we propose the Ansatz which makes the N=4 superconformal flatness of the N=4 supergravity curved superspace manifest. The locally (4,4) supersymmetric TM-I matter couplings, with the potential terms resulting from spontaneous supersymmetry breaking, are constructed. We also find the full (4,4) superconformally invariant (improved) TM-II matter action. The latter can be extended to the (4,4) locally supersymmetric Liouville action which is suitable for describing (4,4) supersymmetric non-critical strings.