On the sigma-model of deformed special geometry

TL;DR

This paper explores how deformations, including non-holomorphic terms, affect the geometry of sigma-models in N=2 supersymmetric theories, revealing that such deformations typically lead to non-Kähler geometries.

Contribution

It introduces a framework for analyzing deformed special geometry in sigma-models, incorporating non-holomorphic deformations and intrinsic torsion analysis.

Findings

Deformed geometries are generally non-Kähler.

The Hesse potential effectively describes the deformed sigma-model.

Intrinsic torsion classes characterize the geometry of the deformed models.

Abstract

We discuss the deformed sigma-model that arises when considering four-dimensional N=2 abelian vector multiplets in the presence of an arbitrary chiral background field. In addition, we allow for a class of deformations of special geometry by non-holomorphic terms. We analyze the geometry of the sigma-model in terms of intrinsic torsion classes. We show that, generically, the deformed geometry is non-Kahler. We illustrate our findings with an example. We also express the deformed sigma-model in terms of the Hesse potential that underlies the real formulation of special geometry.