Hessian geometry and the holomorphic anomaly

TL;DR

This paper introduces a geometric framework based on Hessian geometry that incorporates higher derivative corrections in N=2 vector multiplet actions, linking the holomorphic anomaly to integrability conditions of a Hesse potential.

Contribution

It develops a deformed special Kahler geometry framework that explains the holomorphic anomaly via integrability conditions of a Hesse potential.

Findings

Formulation of an enlarged scalar manifold with complex deformation parameter

Characterization of a deformed special Kahler geometry

Derivation of the holomorphic anomaly equation from geometric integrability

Abstract

We present a geometrical framework which incorporates higher derivative corrections to the action of N = 2 vector multiplets in terms of an enlarged scalar manifold which includes a complex deformation parameter. This enlarged space carries a deformed version of special Kahler geometry which we characterise. The holomorphic anomaly equation arises in this framework from the integrability condition for the existence of a Hesse potential.