Duality relations for overlaps of integrable boundary states in AdS/dCFT

The encoding of all possible sets of Bethe equations for a spin chain with SU(N vertical bar 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.

Automated summary

This research aims to express spin chain overlaps using Q-functions, and by determining the transformation properties of the overlaps under fermionic and bosonic dualities, it allows moving between different descriptions of the spin chain encoded in the QQ-system.