A generalized method for all-loop results in $\lambda$-models

TL;DR

This paper presents a comprehensive method to compute all-loop anomalous dimensions in asymmetric $ ext{lambda}$-models, leveraging geometric and auxiliary interaction techniques, applicable to various deformed models.

Contribution

It introduces a novel all-order calculation framework for anomalous dimensions in $ ext{lambda}$-models with general deformation matrices, extending previous partial results.

Findings

Derived explicit all-order anomalous dimensions for specific models.

Validated the method against known special cases.

Provided new insights into the RG flow of deformed models.

Abstract

We compute the anomalous dimension of the single current operator in the case of single and doubly deformed asymmetric $\lambda$-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.