N=(4,4), 2D supergravity in SU(2)xSU(2) harmonic superspace

TL;DR

This paper develops the framework for conformal N=(4,4) 2D supergravity within harmonic superspace, identifying a new minimal supermultiplet and exploring its truncations and couplings.

Contribution

It introduces a novel off-shell N=(4,4) supergravity multiplet in harmonic superspace and analyzes its gauge structure, constraints, and matter couplings.

Findings

Derived the irreducible N=(4,4) Weyl supermultiplet in harmonic superspace.

Constructed various truncations and couplings to matter multiplets.

Discovered new off-shell gauge representations at the linearized level.

Abstract

We work out the basics of conformal $N=(4,4)$, 2D supergravity in the $N=(4,4)$, 2D analytic harmonic superspace with two independent sets of harmonic variables. We define the relevant most general analytic superspace diffeomorphism group and show that in the flat limit it goes over into the ``large'' $N=(4,4)$, 2D superconformal group. The basic objects of the supergravity considered are analytic vielbeins covariantizing two analyticity-preserving harmonic derivatives. For self-consistency they should be constrained in a certain way. We solve the constraints and show that the remaining irreducible field content in a WZ gauge amounts to a new short $N=(4,4)$ Weyl supermultiplet. As in the previously known cases, it involves no auxiliary fields and the number of remaining components in it coincides with the number of residual gauge invariances. We discuss various truncations of this ``master'' conformal supergravity group and its compensations via couplings to $N=(4,4)$ superconformal matter multiplets. Besides recovering the standard minimal off-shell $N=(4,4)$ conformal and Poincar\'e supergravity multiplets, we find, at the linearized level, several new off-shell gauge representations.