Abstract
We construct two-parameter families of integrable λ-deformations of two-dimensional field theories. These interpolate between a CFT (a WZW/gauged WZW model) and the non-Abelian T-dual of a principal chiral model on a group/symmetric coset space. In examples based on the SU(2) WZW model and the SU(2)/U(1) exact coset CFT, we show that these deformations are related to bi-Yang–Baxter generalisations of η-deformations via Poisson–Lie T-duality and analytic continuation. We illustrate the quantum behaviour of our models under RG flow. As a byproduct we demonstrate that the bi-Yang–Baxter σ-model for a general group is one-loop renormalisable.
Highlights
Introduction and motivationOne of the most powerful tools available to the modern holographic practitioner is integrability
In this paper we will construct a two-parameter family of integrable λ-deformations in which λab acquires some off-diagonal antisymmetric components
We present in Appendix C an explicit demonstration of its integrality in the hope that the reader may find, as we did, it to be illuminating
Summary
One of the most powerful tools available to the modern holographic practitioner is integrability. The deformation parameter is given in terms of the radius of the PCM κ2, and the WZW level k, by λ This construction was initiated in [9] (where more emphasis was given to the cases corresponding to group spaces), and performed more rigorously for symmetric coset spaces in [10] and further generalised to semi-symmetric spaces and applied to the AdS5 ×S5 superstring in [11]. As shown for the case of principal chiral models in [6], the YB σ -models take precisely the form of one-half of a PL T-dual related pair This PL action has been considered in the case of symmetric spaces [18] where it was shown that it leads to an equivalence between the Hamiltonian of the YB σ -model on the real branch A two-dimensional example based on SU(2)/U (1) has been provided in [19] and conjectured to hold in general
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