Gauged WZW-type theories and the all-loop anisotropic non-Abelian Thirring model

Abstract

We study what we call the all-loop anisotropic bosonized Thirring σ-model. This interpolates between the WZW model and the non-Abelian T-dual of the principal chiral model for a simple group. It has an invariance involving the inversion of the matrix parametrizing the coupling constants. We compute the general renormalization group flow equations which assume a remarkably simple form and derive its properties. For symmetric couplings, they consistently truncate to previous results in the literature. One of the examples we provide gives rise to a first order system of differential equations interpolating between the Lagrange and the Darboux-Halphen integrable systems.

Integrable flows between exact CFTs

“…The computation of the renormalization group (RG) flow equations that are exact in λ but for large k using gravitational methods was performed in [4,5]. The results agree with those obtained from field theoretical methods in the past [6,7] and more recently in [8].…”

An integrable deformation of the AdS5×S5superstring

“…See [27,42,43] for more recent and general calculations of this type. 4 In counting the dimension of configuration space fermions effectively contribute As it stands, therefore, there is no matching between the number of bosonic and fermionic degrees-of-freedom as would be required to have a consistent string worldsheet theory.…”

A new class of integrable deformations of CFTs

“…Similarly to λ-deformations, we have revealed the non-petrurbative symmetry (2.14) in the parameter space of λ 1 and λ 2 , albeit for large levels k. This should be instrumental in studying the quantum behaviour of these models along the lines of the similar treatment that we have undergone for the λ-deformations. In particular, one may follow and appropriately modify the beta-function computations in [2,3] using gravitational methods, as well as the computation of the current and anomalous dimensions of primary operators in [28,29] using CFT methods and the non-perturbative symmetry (1.9).…”

“…Since (1.6) is no-longer corresponding to a conformal background, it is expected that the matrix elements λ ab will run under the renormalization group (RG) flow. Indeed, the computation of the corresponding RG flow equations using gravitational methods was performed in [2,3] and is in agreement with results from field theoretical methods [8][9][10]. Furthermore, it was shown that these models, named generically as λ-deformed, can be embedded in specific cases of low dimensionality to supergravity [11][12][13][14][15], while their relation to η-deformations for group and coset spaces introduced in [16][17][18] and [19][20][21] respectively, via Poisson-Lie T-duality [22] and appropriate analytic continuations, was uncovered in [23][24][25][26][27].…”

“…However, unlike the λ-deformed action (1.6) these current bilinears belong to different WZW models. 3 Curiously, if one of the matrices λ i is identically equal to zero the above expression is exact in the other matrix. Note that this particular case has been examined before in [38,39].…”