Abstract
We study quantum aspects of the recently constructed doubly λ-deformed σ-models representing the effective action of two WZW models interacting via current bilinears. We show that although the exact beta-functions and current anomalous dimensions are identical to those of the λ-deformed models, this is not true for the anomalous dimensions of generic primary field operators in accordance with the fact that the two models differ drastically. Our proofs involve CFT arguments, as well as effective σ-model action and gravity calculations.
Highlights
Introduction and conclusionsRecently, a new class of integrable σ -model theories based on current algebra theories for a general semisimple group G was constructed in [1]
A new class of integrable σ -model theories based on current algebra theories for a general semisimple group G was constructed in [1]
This was achieved by utilizing a left– right asymmetric gauging of two independent WZW models both at the same positive integer
Summary
A new class of integrable σ -model theories based on current algebra theories for a general semisimple group G was constructed in [1]. We employ the all-loop effective action of these doubly-deformed CFTs obtained in [1] (provided in (1.1) below) by considering the Lagrangian of the quantum fluctuations around a classical constant background solution along the lines of [5] and for the case of isotropic coupling matrices, i.e. proportional to the identity. We summarize the main results of the present paper: At the level of current operators the correlation functions of our model factorize and can be obtained from two copies each of which corresponds to a usual λ-deformed model, one with coupling matrix λ1 and the other with coupling λ2 This implies the remarkable fact that the running of each of the couplings λ1 and λ2 is the same as in the case of the single λ-deformations computed in [6] and [7] (see (2.5) and (4.20), respectively). We will derive the exact scaling dimensions of the affine primary operators of the model under consideration
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