All-loop anomalous dimensions in integrable λ-deformed σ-models

Georgiou, George; Konstantinos, Sfetsos; Siampos, Konstadinos (2015). All-loop anomalous dimensions in integrable λ-deformed σ-models. Nuclear physics. B, 901, pp. 40-58. North Holland 10.1016/j.nuclphysb.2015.10.007

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We calculate the all-loop anomalous dimensions of current operators in λ-deformed σ-models. For the isotropic integrable deformation and for a semi-simple group G we compute the anomalous dimensions using two different methods. In the first we use the all-loop effective action and in the second we employ perturbation theory along with the Callan–Symanzik equation and in conjunction with a duality-type symmetry shared by these models. Furthermore, using CFT techniques we compute the all-loop anomalous dimension of bilinear currents for the isotropic deformation case and a general G . Finally we work out the anomalous dimension matrix for the cases of anisotropic SU(2) and the two couplings, corresponding to the symmetric coset G/H and a subgroup H, splitting of a group G.

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