Poisson-Lie T-plurality

TL;DR

This paper extends the formalism of Poisson-Lie T-duality to more complex Drinfeld doubles, corrects a key aspect of the dilaton shift, and explicitly constructs duals for certain space-times, confirming their conformal invariance.

Contribution

It generalizes Poisson-Lie T-duality to multiple decompositions of Drinfeld doubles, corrects the dilaton shift formula, and classifies all conformal T-duals of three-dimensional space-times.

Findings

Derived all conformal Poisson-Lie T-duals for 3D space-times.

Explicitly constructed duals for Bianchi type V space-time.

Confirmed duals satisfy string equations of motion.

Abstract

We extend the path-integral formalism for Poisson-Lie T-duality to include the case of Drinfeld doubles which can be decomposed into bi-algebras in more than one way. We give the correct shift of the dilaton, correcting a mistake in the litterature. We then use the fact that the six dimensional Drinfeld doubles have been classified to write down all possible conformal Poisson-Lie T-duals of three dimensional space times and we explicitly work out two duals to the constant dilaton and zero anti-symmetric tensor Bianchi type V space time and show that they satisfy the string equations of motion. This space-time was previously thought to have no duals because of the tracefulness of the structure constants.