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arXiv · 1509.02946

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

George Georgiou·Konstantinos Sfetsos·Konstantinos Siampos
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Abstract

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 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 $G$.

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George Georgiou, Konstantinos Sfetsos, Konstantinos Siampos. 2016-04-28. All-loop anomalous dimensions in integrable $λ$-deformed $σ$-models. https://doi.org/10.1016/j.nuclphysb.2015.10.007

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