Abstract
Using considerations based on the thermodynamical Bethe ansatz as well as the 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 mathfrak{so} (5). The latter play the role of boundary states in a domain wall version of mathcal{N} = 4 SYM theory which has non-vanishing, SO(5) symmetric vacuum expectation values on one side of a codimension 1 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.
Highlights
Introduction and summaryA surprisingly fruitful cross-fertilization between holography and statistical physics has taken place in recent years due to a common interest in overlaps between Bethe eigenstates of integrable systems and states which are not expressible in terms of eigenstates
Using considerations based on the thermodynamical Bethe ansatz as well as the 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 boundary states in question take the form of matrix product states generated by matrices which are related to the generators of some irreducible representation of a Lie group
Summary
A surprisingly fruitful cross-fertilization between holography and statistical physics has taken place in recent years due to a common interest in overlaps between Bethe eigenstates of integrable systems and states which are not expressible in terms of eigenstates. The vacua on the two sides of the wall differ by some of the scalar fields taking nonzero vacuum expectation values (vevs) on one side, say for x3 > 0 These field theories constitute defect conformal field theories (dCFTs) and are dual to probe brane systems with configurations of background gauge fields which lead to nontrivial flux or instanton number [15,16,17,18,19,20,21]. All the overlaps which were known in closed form at that time were compatible with this definition of integrability This was in particular true for the dCFT dual to the 1/2 supersymmetric D3-D5 probe brane system with background gauge field flux where a closed expression for all the one-point functions of the scalar sector had been found [13]. Where λ is the ’t Hooft coupling, proportional to the inverse string tension according to the AdS/CFT dictionary
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