N=(4,4) Vector Multiplets on Curved Two-Manifolds

TL;DR

This paper investigates conditions for maintaining N=(4,4) supersymmetry on curved two-dimensional spaces, deriving transformation laws and actions for vector multiplets, with explicit solutions on the two-sphere.

Contribution

It provides the first detailed derivation of off-shell Abelian vector multiplet actions preserving N=(4,4) supersymmetry on curved 2d manifolds, including explicit solutions on the sphere.

Findings

Derived supersymmetry transformation laws and invariant actions.

Identified conditions for supersymmetry preservation on curved backgrounds.

Explicit solution of supersymmetry conditions on the two-sphere.

Abstract

We study the necessary conditions for preserving N=(4,4) supersymmetry on curved 2d backgrounds, following the strategy of Dumitrescu, Festuccia, and Seiberg. We derive the transformation laws and invariant action for off-shell Abelian vector multiplets. An explicit solution of the supersymmetry conditions is found on the round two-sphere.