On uniqueness of T-duality with spectators

TL;DR

This paper explores how nonabelian T-duality in nonlinear sigma models depends on the choice of target space isometries and the placement of group units, revealing potential ambiguities in the duality process.

Contribution

It demonstrates that T-duals can depend on the specific identification of isometry groups and the position of group units, highlighting a nuanced aspect of T-duality.

Findings

T-duals may vary with different isometry group identifications.

Dependence on the position of group units affects T-duality outcomes.

Coordinate transformations may not fully eliminate this dependence.

Abstract

We investigate the dependence of nonabelian T-duality on various identification of the group of target space isometries of nonlinear sigma models with its orbits, i.e. with respect to the location of the group unit on manifolds invariant under the isometry group. We show that T-duals constructed by isometry groups of dimension less than the dimension of the (pseudo)riemannian manifold may depend not only on the initial metric but also on the choice of manifolds defining positions of group units on each of the submanifold invariant under the isometry group. We investigate whether this dependence can be compensated by coordinate transformation.