Abstract
We show that the CFT with symmetry group {G}_{k_1}times {G}_{k_2}times cdots times {G}_{k_n} consisting of WZW models based on the same group G, but at arbitrary integer levels, admits an integrable deformation depending on 2(n − 1) continuous parameters. We derive the all-loop effective action of the deformed theory and prove integrability. We also calculate the exact in the deformation parameters RG flow equations which can be put in a particularly simple compact form. This allows a full determination and classification of the fixed points of the RG flow, in particular of those that are IR stable. The models under consideration provide concrete realizations of integrable flows between CFTs. We also consider non-Abelian T-duality type limits.
Highlights
The construction is certain conformal field theories (CFTs) of the WZW type perturbed by current bilinear operators with the currents belonging either to the same and/or different groups
We show that the CFT with symmetry group Gk1 × Gk2 × · · · × Gkn consisting of WZW models based on the same group G, but at arbitrary integer levels, admits an integrable deformation depending on 2(n−1) continuous parameters
The λ-deformed models are related via Poisson-Lie T-duality, which has been introduced for group spaces in [41] and extended for coset spaces in [42], and appropriate analytic continuations to the η-deformed models
Summary
We construct the effective actions of our model and derive the corresponding equations of motion. In order to obtain the σ-model and to show integrability we should integrate out the gauge fields These are not dynamical and appear only quadratically in the action. Where as usual we have defined D±gi = ∂±gi−[A(±i), gi] and where we note that the transpose in λ−ijT , as well as the inverses refer only to the suppressed group indices and not on the space of couplings with indices i, j. Substituting the values for the gauge fields in the action (2.4) we obtain the following σ-model n. It is the most general action that can be construct using the same group G for all couplings. The inversion of the above matrices in the coupling space will be done explicitly for the case of integrable models
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