Abstract
Two-dimensional σ-models corresponding to coset CFTs of the type (gˆk⊕hˆℓ)/hˆk+ℓ admit a zoom-in limit involving sending one of the levels, say ℓ, to infinity. The result is the non-Abelian T-dual of the WZW model for the algebra gˆk with respect to the vector action of the subalgebra h of g. We examine modular invariant partition functions in this context. Focusing on the case with g=h=su(2) we apply the above limit to the branching functions and modular invariant partition function of the coset CFT, which as a whole is a delicate procedure. Our main concrete result is that such a limit is well defined and the resulting partition function is modular invariant.
Highlights
In this paper we consider quantum aspects of non-Abelian T-duality in Wess-ZuminoWitten (WZW) [1, 2] models
We find that by taking two inequivalent limits in target space, we can associate this partition function with two different geometries
While we have not checked explicitly, the form of the limiting partition function we find is highly suggestive of the same interpretation
Summary
In this paper we consider quantum aspects of non-Abelian T-duality in Wess-ZuminoWitten (WZW) [1, 2] models. We find that by taking two inequivalent limits in target space, we can associate this partition function with two different geometries This is suggestive of a duality between these two backgrounds, which is not the original non-Abelian T-duality, but something else, a kind of large-level equivalence. Our approach to modular invariants for backgrounds related to non-Abelian T-duality was first established in [5] by taking a limit in gauged WZW models (corresponding to coset CFTs), involving as a basic ingredient large level. In order to introduce our approach and method, we start with a different (albeit related and much simpler) limit in WZW models
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