N = (4, 4) vector multiplets on curved two-manifolds.

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 offshell Abelian vector multiplets. An explicit solution of the supersymmetry conditions is found on the round two-sphere. [ABSTRACT FROM AUTHOR]