N=2 symplectic reparametrizations in a chiral background

TL;DR

The work analyzes how $N=2$ vector multiplet theories with a chiral background transform under symplectic dualities, showing that duality acts as canonical transformations on the period vector and induces a transformed prepotential $\tilde{F}(\tilde{X})$, while holomorphic combinations like $F(X)-\tfrac{1}{2}X^I F_I(X)$ remain holomorphic. Through an explicit two-vector multiplet example, it clarifies when symplectic reparametrizations are symmetries versus reparametrizations and how charges constrain duality bases. Extending to backgrounds, the paper derives a hierarchy of holomorphic-covariant coefficient functions $F^{(n)}(X,A)$ that transform as symplectic functions and satisfy a holomorphic anomaly equation akin to the BCOV framework, highlighting the conflict between holomorphy and covariant duality. These results connect duality symmetries, background fields, and holomorphic anomalies in $N=2$ theories, with implications for string compactifications and topological amplitudes.

Abstract

We study the symplectic reparametrizations that are possible for theories of N=2 supersymmetric vector multiplets in the presence of a chiral background and discuss some of their consequences. One of them concerns an anomaly arising from a conflict between symplectic covariance and holomorphy.