Integrable branes in generalized $\lambda$-deformations

TL;DR

This paper investigates integrable boundary conditions and their geometric interpretation as D-branes in generalized lambda-deformations of product spaces, confirming known conformal branes persist along RG flows and analyzing their properties.

Contribution

It identifies and characterizes integrable D-brane geometries in generalized lambda-deformed models, extending known conformal branes to RG flow regimes.

Findings

Known conformal branes solve boundary conditions in the models.

These branes include G-conjugacy classes, twisted conjugacy classes, and permutation branes.

The properties of these branes are analyzed in interpolating backgrounds.

Abstract

We search for integrable boundary conditions and their geometric interpretation as $D$-branes, in models constructed as generalized $\lambda$-deformations of products of group- and coset-spaces. Using the sigma-model approach, we find that all the conformal brane geometries known in the literature for a product of WZW models solve the corresponding boundary conditions, thus persisting as integrable branes along the RG flows of our sigma-models. They consist of the well known $G$-conjugacy classes, twisted $G$-conjugacy classes by a permutation automorphism (permutation branes) and generalized permutation branes. Subsequently, we study the properties of the aforementioned brane geometries, especially of those embedded in the backgrounds interpolating between the UV and IR fixed points.