Overlaps and Fermionic Dualities for Integrable Super Spin Chains

TL;DR

This paper studies overlaps in integrable super spin chains related to the AdS/CFT correspondence, focusing on how these overlaps transform under fermionic dualities and their implications for boundary states and one-point functions.

Contribution

It determines the transformation properties of overlap formulas under fermionic dualities in super Lie algebra Dynkin diagrams, enabling consistent comparisons across different representations.

Findings

Overlap formulas depend on the choice of Dynkin diagram.

Fermionic dualities relate different overlap expressions.

Consistent mapping between overlap formulas for k=1 cases.

Abstract

The psu(2,2|4) integrable super spin chain underlying the AdS/CFT correspondence has integrable boundary states which describe set-ups where k D3-branes get dissolved in a probe D5-brane. Overlaps between Bethe eigenstates and these boundary states encode the one-point functions of conformal operators and are expressed in terms of the superdeterminant of the Gaudin matrix that in turn depends on the Dynkin diagram of the symmetry algebra. The different possible Dynkin diagrams of super Lie algebras are related via fermionic dualities and we determine how overlap formulae transform under these dualities. As an application we show how to consistently move between overlap formulae obtained for k=1 from different Dynkin diagrams.