# Integrable asymmetric $\lambda$-deformations

## TL;DR

This paper develops new integrable deformations of asymmetrically gauged WZW models, verifying their classical integrability, analyzing their beta functions, and constructing compatible D-brane configurations, with a detailed example involving the cigar geometry.

## Contribution

It introduces a modified gauging procedure for asymmetric lambda-deformations, extending integrability and D-brane construction methods in these models.

## Key findings

- Classical integrability of the deformed models is verified.
- One-loop beta functions for the deformation parameters are derived.
- Explicit integrable D-brane configurations are constructed in the deformed models.

## Abstract

We construct integrable deformations of the $\lambda$-type for asymmetrically gauged WZW models. This is achieved by a modification of the Sfetsos gauging procedure to account for a possible automorphism that is allowed in $G/G$ models. We verify classical integrability, derive the one-loop beta function for the deformation parameter and give the construction of integrable D-brane configurations in these models. As an application, we detail the case of the $\lambda$-deformation of the cigar geometry corresponding to the axial gauged $SL(2,R)/U(1)$ theory at large $k$. Here we also exhibit a range of both A-type and B-type integrability preserving D-brane configurations.