A generalized method for all-loop results in λ-models

Abstract

We compute the anomalous dimension of the single current operator in the case of single and doubly deformed asymmetric λ-models with a general deformation matrix. Our method uses the underlying geometry of the coupling space, as well as an auxiliary group interaction, which completely decouples from the asymmetric model in a specific limit, consistent with the Renormalization Group flow. Our results are valid to all orders in the deformation parameters and leading order to the levels of the underlying current algebras. We specialize our general result to several models of particular interest that have been constructed in the literature and for which these anomalous dimensions were not known.

RG flows of integrable σ-models and the twist function

“…A natural playground to test this conjecture consists of integrable coupled deformed σ-models. In the case of λ-deformations, such integrable coupled models have been introduced in [15,[30][31][32], their one-loop renormalization group flows have been investigated in [15,[31][32][33] and their twist functions computed in [17]. The most general combination of integrable λ-and Yang-Baxter deformations of the coupled σ-model studied in this article has been constructed in [34].…”

RG flows of integrable $σ$-models and the twist function

“…A natural playground to test this conjecture consists of integrable coupled deformed σ-models. In the case of λ-deformations, such integrable coupled models have been introduced in [30,15,31,32], their one-loop renormalization group flows have been investigated in [15,[31][32][33] and their twist functions computed in [17]. The most general combination of integrable λ-and Yang-Baxter deformations of the coupled σ-model studied in this article has been constructed in [34].…”

$λ$-deformations in the upper-half plane

“…These efforts allowed the exact determination of two-and three-point functions of current, composite current-bilinear and primary fields and of their anomalous dimensions [36,31,37,38]. A rather distinct approach in performing computations in this context was put forward in [39].…”