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Determinant form of correlators in high rank integrable spin chains via separation of variables

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Nikolay Gromov, Fedor Levkovich-Maslyuk, Paul Ryan

Original languageEnglish
Article number169
JournalJournal of High Energy Physics
Volume2021
Issue number5
Early online date19 May 2021
DOIs
Accepted/In press28 Apr 2021
E-pub ahead of print19 May 2021
PublishedMay 2021

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Publisher Copyright: © 2021, The Author(s). Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

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Abstract

In this paper we take further steps towards developing the separation of variables program for integrable spin chains with gl(N) symmetry. By finding, for the first time, the matrix elements of the SoV measure explicitly we were able to compute correlation functions and wave function overlaps in a simple determinant form. In particular, we show how an overlap between on-shell and off-shell algebraic Bethe states can be written as a determinant. Another result, particularly useful for AdS/CFT applications, is an overlap between two Bethe states with different twists, which also takes a determinant form in our approach. Our results also extend our previous works in collaboration with A. Cavaglia and D. Volin to general values of the spin, including the SoV construction in the higher-rank non-compact case for the first time.

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