Tensor supermultiplets and toric quaternion-Kahler geometry

TL;DR

This paper explores the connection between quaternion-Kahler geometry and superconformal tensor multiplet theories, providing a method to construct specific eight-dimensional metrics with multiple symmetries using linear PDEs.

Contribution

It introduces a new construction of eight-dimensional quaternion-Kahler metrics with three abelian isometries via solutions to linear PDEs, linking geometry with superconformal theories.

Findings

Constructed explicit eight-dimensional quaternion-Kahler metrics with three abelian isometries.

Established a relation between these metrics and superconformal tensor multiplet theories.

Provided a set of linear PDEs to generate such metrics.

Abstract

We review the relation between 4n-dimensional quaternion-Kahler metrics with n+1 abelian isometries and superconformal theories of n+1 tensor supermultiplets. As an application we construct the class of eight-dimensional quaternion-Kahler metrics with three abelian isometries in terms of a single function obeying a set of linear second-order partial differential equations.