Exact overlaps for all integrable two-site boundary states of gl $$ \mathfrak{gl} $$ (N) symmetric spin chains

Abstract

Abstract We find closed formulas for the overlaps of Bethe eigenstates of gl $$ \mathfrak{gl} $$ (N) symmetric spin chains and integrable boundary states. We derive the general overlap formulas for gl $$ \mathfrak{gl} $$ (M) ⊕ gl $$ \mathfrak{gl} $$ (N − M) symmetric boundary states and give a well-established conjecture for the sp $$ \mathfrak{sp} $$ (N) symmetric case. Combining these results with the previously derived so $$ \mathfrak{so} $$ (N) symmetric formula, now we have the overlap functions for all integrable boundary states of the gl $$ \mathfrak{gl} $$ (N) spin chains which are built from two-site states. The calculations are independent from the representations of the quantum space therefore our formulas can be applied for the SO(6) and the alternating SU(4) spin chains which describe the scalar sectors of N $$ \mathcal{N} $$ = 4 super Yang-Mills and ABJM theories which are important application areas of our results.

Keywords

• Bethe Ansatz
• Lattice Integrable Models
• AdS-CFT Correspondence
• Wilson, ’t Hooft and Polyakov loops