T-duality and HKT manifolds

TL;DR

This paper explores how T-duality and conformal rescaling affect four-dimensional HKT geometries, revealing new geometric families and supersymmetric models with specific properties.

Contribution

It demonstrates the generation of new HKT geometries via T-duality and conformal rescaling, and identifies ultraviolet-finite supersymmetric sigma models that lack conformal invariance.

Findings

Conformal factors satisfy a modified harmonic equation.

Non-commutative groups act on HKT geometries.

New families of HKT geometries with tri-holomorphic Killing vectors are constructed.

Abstract

We examine conformal rescaling and T-duality in the context of four-dimensional HKT geometries. The closure of the torsion forces the conformal factor to satisfy a modified harmonic equation. Because of this equation the conformal factors form non-commutative groups acting on the HKT geometries. Using conformal rescalings and T-duality transformations we generate from flat space new families of HKT geometries with tri-holomorphic Killing vectors. We also find ultraviolet-finite (4,0) supersymmetric sigma models which are not conformally invariant.