Analytic approach to boundary integrability with application to mixed-flux $AdS_3 \times S^3$

TL;DR

The paper addresses boundary integrability in two-dimensional sigma-models, focusing on mixed NSNS/RR flux in $AdS_3\times S^3$. It introduces an intrinsic divisor-matching criterion on the bulk Lax connection ${\cal L}(\mathsf{x})$ to fix the reflection map $\rho(\mathsf{x})$ and gauge $U$, enabling a Sklyanin-type double-row construction without relying on bulk parity. For the mixed-flux bosonic model, it identifies two integrable boundary branches: one with D-branes wrapping twisted conjugacy classes, where the flux appears entirely in the dynamical reflection data $K_{\sigma_\star}(\mathsf{x})$, and a WZW-point branch that recovers conformal branes, linking to BCFT and conformal perturbation theory. The framework provides a concrete analytic bridge between classical boundary integrability and BCFT in AdS/CFT with finite flux, and offers a path to compare integrability-based reflection data with conformal perturbations away from the exact WZW point.

Abstract

Boundary integrability provides rare analytic control over field theories in the presence of an interface, from quantum impurity problems to open string dynamics. We develop an analytic framework for integrable boundaries in two-dimensional sigma-models that determines admissible reflection maps directly from the meromorphic Lax connection. Applying it to open strings on $AdS_3\times S^3$ with mixed NSNS and RR flux, we find two branches of integrable boundary conditions. One branch admits D-branes wrapping twisted conjugacy classes on $SU(1,1)\times SU(2)$, with the mixed-flux deformation encoded entirely into dynamical boundary data. At the exactly solvable WZW point these coincide with the conformal D-branes, providing a natural link to conformal perturbation theory.