Abstract
We prove that the doubly λ-deformed σ-models, which include integrable cases, are canonically equivalent to the sum of two single λ-deformed models. This explains the equality of the exact β-functions and current anomalous dimensions of the doubly λ-deformed σ-models to those of two single λ-deformed models. Our proof is based upon agreement of their Hamiltonian densities and of their canonical structure. Subsequently, we show that it is possible to take a well defined non-Abelian type limit of the doubly-deformed action. Last, but not least, by extending the above, we construct multi-matrix integrable deformations of an arbitrary number of WZW models.
Highlights
Introduction and resultsA new class of integrable theories based on current algebras for a semi-simple group was recently constructed [1]
We prove that the doubly λ-deformed σ -models, which include integrable cases, are canonically equivalent to the sum of two single λ-deformed models
The construction of the single λ-deformed σ -model starts by considering the sum of a gauged WZW and a PCM for a group G, defined with group elements g and g, respectively and gauging the global symmetry [2]
Summary
A new class of integrable theories based on current algebras for a semi-simple group was recently constructed [1]. This happens if these models are forced to obey the cyclic symmetry property or if they are infinitely many, resembling in structure either a closed or an infinitely open spin chain.
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