T-Duality for Coset Models

We construct dual Lagrangians for G/H models in two space-time dimensions for arbitrary Lie groups G and H ⊂ 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 G̃ dual to G, and the gauge group H (which, in general, is not a subgroup of G̃) acts nonlinearly on G̃. 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.