No abstract

Integrable boundary states can be built up from pair annihilation amplitudes called K-matrices. These amplitudes are related to mirror reflections and they both satisfy Yang Baxter equations, which can be twisted or untwisted. We relate these two notions to each other and show how they are fixed by the unbroken symmetries, which, together with the full symmetry, must form symmetric pairs. We show that the twisted nature of the K-matrix implies specific selection rules for the overlaps. If the Bethe roots of the same type are paired the overlap is called chiral, otherwise it is achiral and they correspond to untwisted and twisted K-matrices, respectively. We use these findings to develop a nesting procedure for K-matrices, which provides the factorizing overlaps for higher rank algebras automatically. We apply these methods for the calculation of the simplest asymptotic all-loop 1-point functions in AdS/dCFT. In doing so we classify the solutions of the YBE for the K-matrices with centrally extended $$ \mathfrak{su} $$ su (2|2)c symmetry and calculate the generic overlaps in terms of Bethe roots and ratio of Gaudin determinants.

Using considerations based on the thermodynamical Bethe ansatz as well representation theory of twisted Yangians we derive an exact expression for the overlaps between the Bethe eigenstates of the SO(6) spin chain and matrix product states built from matrices whose commutators generate an irreducible representation of so(5). The latter play the role of boundary states in a domain wall version of N = 4 SYM theory which has nonvanishing, SO(5) symmetric vacuum expectation values on one side of a co-dimension one wall. This theory, which constitutes a defect CFT, is known to be dual to a D3-D7 probe brane system. We likewise show that the same methodology makes it possible to prove an overlap formula, earlier presented without proof, which is of relevance for the similar D3-D5 probe brane system.

We formulate and close the boundary state bootstrap for factorizing K-matrices in AdS/CFT. We found that there are no boundary degrees of freedom in the boundary bound states, merely the boundary parameters are shifted. We use this family of boundary bound states to describe the D3-D5 system for higher dimensional matrix product states and provide their asymptotic overlap formulas. In doing so we generalize the nesting for overlaps of matrix product states and Bethe states.