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

Abstract

Abstract We study the integrable crosscap states of the integrable quantum spin chains and we classify them for the gl $$ \mathfrak{gl} $$ (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.

Keywords

• Bethe Ansatz
• Lattice Integrable Models
• AdS-CFT Correspondence