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

Abstract

A bstract We study the integrable crosscap states of the integrable quantum spin chains and we classify them for the $$ \mathfrak{gl} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>gl</mml:mi> </mml:math> ( 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.

Topics & Concepts