Abstract
We compute the 2- and 3-point functions of currents and primary fields of λ-deformed integrable σ-models characterized also by an integer k. Our results apply for any semisimple group G, for all values of the deformation parameter λ and up to order 1/k. We deduce the OPEs and equal-time commutators of all currents and primaries. We derive the currents' Poisson brackets which assume Rajeev's deformation of the canonical structure of the isotropic PCM, the underlying structure of the integrable λ-deformed σ-models. We also present analogous results in two limiting cases of special interest, namely for the non-Abelian T-dual of the PCM and for the pseudodual model.
Highlights
Introduction and motivationOne of the most intriguing conjectures in modern theoretical physics is the AdS/conformal field theory (CFT) correspondence [1] which, in its initial form, states the equivalence between type-IIB superstring theory on the AdS5 × S5 background and the maximally supersymmetric field theory in fourG
Since the above non-Abelian and pseudodual limits exist at the action level, we expect that physical quantities such as the β-function and the anomalous dimensions of various operators should have a well defined limit as well
In this work we have computed all possible two- and three-point functions of current and primary field operators for the λ-deformed integrable σ -models. These models are characterized by the deformation parameter λ, as well as by the integer level k of the WZW model
Summary
One of the most intriguing conjectures in modern theoretical physics is the AdS/CFT correspondence [1] which, in its initial form, states the equivalence between type-IIB superstring theory on the AdS5 × S5 background and the maximally supersymmetric field theory in four. We are interested in the non-Abelian Thirring model action (for a general discussion, see [20,21]), namely the WZW two-dimensional conformal field theory (CFT) perturbed by a set of classically marginal operators which are bilinear in the currents k dim G. where the couplings are denoted by the constants λab. The β-functions for the running of couplings under the Renormanization Group (RG) flow using (1.5) were computed in [23,24] and completely agree with the computation of the same RG-flow equations using CFT techniques based on (1.4) in [25] for a single (isotropic) coupling, i.e. when λab = λδab and in [26] for symmetric λab Based on that it was conjectured in [23,24] that (1.5) is the effective action for (1.4) valid to all orders in λ and up to order 1/k. Using path integral techniques and special properties of the WZW model action, it was argued in [27] that the effective action of the non-Abelian Thirring model (not known at the time) should be invariant under the above duality-type symmetry (λ, k) → (λ−1, −k) (for k 1)
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