Spin Chain Overlaps and the Twisted Yangian

TL;DR

This paper derives exact formulas for overlaps between Bethe eigenstates and matrix product states in an SO(6) spin chain, linking integrability, representation theory, and holographic dualities in defect conformal field theories.

Contribution

It provides the first exact overlap expressions for boundary states in an SO(6) spin chain related to defect ${ m N}=4$ SYM and D-brane systems, using thermodynamic Bethe ansatz and twisted Yangian representation theory.

Findings

Derived exact overlap formulas for Bethe states and matrix product states.

Linked overlaps to D3-D7 and D3-D5 probe brane systems in holography.

Validated overlap formulas with implications for defect conformal field theories.

Abstract

Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the $SO(6)$ spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of $\mathfrak{so}(5)$. The latter play the role of boundary states in a domain wall version of ${\cal N}=4$ SYM theory which has non-vanishing, $SO(5)$ symmetric vacuum expectation values on one side of a co-dimension one wall. This theory, which constitutes a defect CFT, is known to be dual to a D3-D7 probe brane system. We likewise show that the same methodology makes it possible to prove an overlap formula, earlier presented without proof, which is of relevance for the similar D3-D5 probe brane system.