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Journal of High Energy Physics

, 2019:52 | Cite as

Separation of variables and scalar products at any rank

  • Andrea Cavaglià
  • Nikolay Gromov
  • Fedor Levkovich-MaslyukEmail author
Open Access
Regular Article - Theoretical Physics
  • 5 Downloads

Abstract

Separation of variables (SoV) is a special property of integrable models which ensures that the wavefunction has a very simple factorised form in a specially designed basis. Even though the factorisation of the wavefunction was recently established for higher rank models by two of the authors and G. Sizov, the measure for the scalar product was not known beyond the case of rank one symmetry. In this paper we show how this measure can be found, bypassing an explicit SoV construction. A key new observation is that the measure for spin chains in a highest-weight infinite dimensional representation of 𝔰𝔩(N) couples Q-functions at different nesting levels in a non-symmetric fashion. We also managed to express a large number of form factors as ratios of determinants in our new approach. We expect our method to be applicable in a much wider setup including the problem of computing correlators in integrable CFTs such as the fishnet theory, \( \mathcal{N} \) = 4 SYM and the ABJM model.

Keywords

Bethe Ansatz Lattice Integrable Models 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  • Andrea Cavaglià
    • 1
  • Nikolay Gromov
    • 1
    • 2
  • Fedor Levkovich-Maslyuk
    • 3
    • 4
    Email author
  1. 1.Mathematics DepartmentKing’s College LondonLondonU.K.
  2. 2.St. Petersburg Nuclear Physics Institute (INP)St. PetersburgRussia
  3. 3.Departement de PhysiqueEcole Normale Superieure/PSL Research University, CNRSParisFrance
  4. 4.Institute for Information Transmission ProblemsMoscowRussia

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