A Note on the Hitchin System in a Background B-field

TL;DR

This paper explores how a background B-field deforms the Hitchin system on a dual torus with punctures, providing explicit solutions and an alternative Higgs branch description relevant to impurity theories.

Contribution

It introduces a B-field deformation of the Hitchin system and constructs explicit solutions via reduction to principal chiral models and deformation quantization.

Findings

Explicit solutions to B-deformed Hitchin equations on the dual torus.

New description of the Higgs branch in terms of B-field deformation.

Connection between Hitchin system deformations and impurity theories.

Abstract

The space of solutions to the Hitchin equations on the dual torus with punctures determines the Higgs branch of certain impurity theories. An alternative description of this Higgs branch is provided, in terms of the proper deformation of Hitchin system with deformation parameter given by a $B$-field. For the dual torus minus the singular points we construct explicit solutions to the B-deformed Hitchin equations by reducing them to principal chiral model equations and then using deformation quantization methods.