N=2 Electric-magnetic duality in a chiral background

TL;DR

This paper proves the consistency of electric-magnetic duality transformations in N=2 vector supermultiplet systems with chiral backgrounds, highlighting the nonholomorphic nature of most duality-related quantities.

Contribution

It establishes the conditions for duality consistency in N=2 systems with chiral backgrounds, including higher-derivative couplings and spurion fields.

Findings

Duality transformations are consistent for N=2 vector multiplets with chiral backgrounds.

Most duality-related quantities do not transform as functions, but as nonholomorphic objects.

Duality transformations are inherently holomorphic, yet the quantities involved are mostly nonholomorphic.

Abstract

We establish the consistency of duality transformations for generic systems of $N=2$ vector supermultiplets in the presence of a chiral background field. This is relevant, for instance, when dealing with spurion fields or when considering higher-derivative couplings of vector multiplets to supergravity. We point out that under duality most quantities do not transform as functions. With few exceptions, true functions are nonholomorphic, even though the duality transformations themselves are holomorphic in nature.