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

TL;DR

This paper develops an analytic method to identify integrable boundary conditions in two-dimensional sigma-models, applied to open strings in $AdS_3 imes S^3$ with mixed flux, revealing new classes of integrable boundaries and connecting to conformal D-branes.

Contribution

It introduces a novel analytic approach for boundary integrability based on the divisor structure of the Lax connection, applicable to complex flux backgrounds.

Findings

Identified two branches of integrable boundaries in $AdS_3 imes S^3$ with mixed flux.

Connected integrable boundary conditions to known conformal D-branes at the WZW point.

Suggested generalizations of lattice constructions for classifying integrable boundaries.

Abstract

Boundary integrability provides rare analytic control over field theories with interfaces, from quantum impurity problems to open string dynamics. We propose an analytic approach for integrable boundaries in two-dimensional sigma-models that determines admissible reflection maps directly from the divisor structure of the Lax connection. Applied to open strings on $AdS_3\times S^3$ with mixed NSNS-RR flux, we find two branches of integrable boundaries: one restricted to pure RR flux, and another admitting D-branes wrapping twisted conjugacy classes for generic flux. At the WZW point, these reduce to the known conformal D-branes, opening a path to comparison with conformal perturbation theory. More broadly, our framework suggests generalisations of standard lattice constructions that may enlarge existing classifications of integrable boundaries.