All-loop anomalous dimensions in integrable \(\lambda\)-deformed \(\sigma\)-models

Abstract

We calculate the all-loop anomalous dimensions of current operators in \(\lambda\)-deformed \(\sigma\)-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 dimensions of bilinear currents for the isotropic deformation case and a general \(G\). Finally we work out the cases of anisotropic \(SU(2)\) and the two coupling, corresponding to the symmetric coset \(G/H\) and a subgroup \(H\), splitting of a group \(G\).