Integrable crosscap states in $\mathfrak{gl}(N)$ spin chains

TL;DR

This paper classifies integrable crosscap states in $rak{gl}(N)$ spin chains, derives exact overlaps with Bethe states, and explores their relevance in AdS/CFT correspondence.

Contribution

It provides a complete classification of integrable crosscap states and derives explicit formulas for their overlaps with Bethe states in $rak{gl}(N)$ models.

Findings

Normalized overlaps are ratios of Gaudin-like determinants.

Sum formulas for off-shell overlaps are established.

Relevant crosscap states are identified for AdS/CFT applications.

Abstract

We study the integrable crosscap states of the integrable quantum spin chains and we classify them for the $\mathfrak{gl}(N)$ symmetric models. We also give a derivation for the exact overlaps between the integrable crosscap states and the Bethe states. The first part of the derivation is to calculate sum formula for the off-shell overlap. Using this formula we prove that the normalized overlaps of the multi-particle states are ratios of the Gaudin-like determinants. Furthermore we collect the integrable crosscap states which can be relevant in the AdS/CFT correspondence.