The non-abelian target space duals of Taub-NUT space

TL;DR

This paper explores non-abelian duality transformations of Taub-NUT space, revealing new solutions and relationships between fixed points, singularities, and duality groups in string theory.

Contribution

It demonstrates non-abelian duality for non-free group actions on Taub-NUT space, uncovering new solutions and the interplay of T-duality procedures.

Findings

U(1) and SO(3) T-dualities commute in this context.

Fixed points correspond to singularities in dual solutions.

Extreme points of the O(1,1) duality group have special significance.

Abstract

We discuss the non-abelian duality procedure for groups which do not act freely. As an example we consider Taub-NUT space, which has the local isometry group $SU(2) \otimes U(1)$. We dualise over the entire symmetry group as well as the subgroups $SO(3)$ and $U(1)$, presenting unusual new solutions to low energy string theory. The solutions obtained highlight the relationship between fixed points of an isometry in one solution and singular points in another. We also find the interesting results that, in this case, the $U(1)$ and $SO(3)$ $T$-duality procedures commute with each other, and that the extreme points of the $O(1,1)$ duality group for the time translations have special significance under the $SO(3)$ T-duality.