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arXiv · 1912.09338

Spin Chain Overlaps and the Twisted Yangian

Marius de Leeuw·Tamás Gombor·Charlotte Kristjansen·Georgios Linardopoulos·Balázs Pozsgay
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Abstract

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 $\mathfrak{so}(5)$. The latter play the role of boundary states in a domain wall version of ${\cal N}=4$ SYM theory which has non-vanishing, $SO(5)$ 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.

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Marius de Leeuw, Tamás Gombor, Charlotte Kristjansen, Georgios Linardopoulos, Balázs Pozsgay. 2019-12-19. Spin Chain Overlaps and the Twisted Yangian. https://doi.org/10.1007/jhep01(2020)176

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