T-Duality for Coset Models

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.

21 pp

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• On strong integrability of the dressing cosets
• Aspects of Quantum Fermionic T-duality
• T-Dualities and Doubled Geometry of the Principal Chiral Model
• Poisson-Lie T-plurality for dressing cosets
• Dual Instantons
• On the classical Integrability of Poisson-Lie T-dual WZW models