T-Duality for Coset Models

TL;DR

This paper develops a general method for constructing dual Lagrangians for coset models in two dimensions, extending to Lie-Poisson duality and providing new insights into dual gauge theories with nonconstant metrics.

Contribution

It introduces a coordinate-independent approach to duality in coset models, generalizes to Lie-Poisson duality, and describes dual systems with nonlinear gauge actions.

Findings

Dual Lagrangians constructed for arbitrary Lie groups G and H.

Dual systems include gauged Higgs models with nonconstant metrics.

Dual descriptions are canonically equivalent to primary models at the current algebra level.

Abstract

We construct dual Lagrangians for $G/H$ models in two space-time dimensions for arbitrary Lie groups $G$ and $H\subset G$. Our approach does not require choosing coordinates on $G/H$, and allows for a natural generalization to Lie-Poisson duality. For the case where the target metric on $G/H$ is induced from the invariant metric on $G$, the dual system is a gauged Higgs model, with a nonconstant metric and a coupling to an antisymmetric tensor. The dynamics for the gauge connection is governed by a $BF$-term. Lie-Poisson duality is relevant once we allow for a more general class of target metrics, as well as for couplings to an antisymmetric tensor, in the primary theory. Then the dual theory is written on a group $\tilde G$ dual to $G$, and the gauge group $H$ (which, in general, is not a subgroup of $\tilde G$) acts nonlinearly on $\tilde G$. The dual system therefore gives a nonlinear realization of a gauge theory. All dual descriptions are shown to be canonically equivalent to the corresponding primary descriptions, at least at the level of the current algebra.