Duality Relations for Overlaps of Integrable Boundary States in AdS/dCFT

TL;DR

This paper develops a universal framework for expressing overlaps between Bethe eigenstates and boundary states in integrable spin chains with SU(N|M) symmetry, relevant for AdS/dCFT, by analyzing duality transformations of Q-functions.

Contribution

It introduces a method to derive overlap formulas using QQ-systems and duality transformations, advancing the understanding of integrable boundary states in AdS/dCFT.

Findings

Derived transformation properties of overlaps under dualities

Established a regularization scheme for singular Bethe roots

Moved towards a universal formula for overlaps in integrable models

Abstract

The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a universal formula in the case of overlaps between Bethe eigenstates and integrable boundary states, of relevance for AdS/dCFT, by determining the transformation properties of the overlaps under fermionic as well as bosonic dualities which allows us to move between any two descriptions of the spin chain encoded in the QQ-system. An important part of our analysis involves introducing a suitable regularization for singular Bethe root configurations.