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Journal of High Energy Physics

, 2016:44 | Cite as

T-system on T-hook: Grassmannian solution and twisted Quantum Spectral Curve

  • Vladimir Kazakov
  • Sébastien LeurentEmail author
  • Dmytro Volin
Open Access
Regular Article - Theoretical Physics

Abstract

We propose an efficient grassmannian formalism for solution of bi-linear finite-difference Hirota equation (T-system) on T-shaped lattices related to the space of highest weight representations of gl(K 1 , K 2|M ) superalgebra. The formalism is inspired by the quantum fusion procedure known from the integrable spin chains and is based on exterior forms of Baxter-like Q-functions. We find a few new interesting relations among the exterior forms of Q-functions and reproduce, using our new formalism, the Wronskian determinant solutions of Hirota equations known in the literature. Then we generalize this construction to the twisted Q-functions and demonstrate the subtleties of untwisting procedure on the examples of rational quantum spin chains with twisted boundary conditions. Using these observations, we generalize the recently discovered, in our paper with N. Gromov, AdS/CFT Quantum Spectral Curve for exact planar spectrum of AdS/CFT duality to the case of arbitrary Cartan twisting of AdS5×S5 string sigma model. Finally, we successfully probe this formalism by reproducing the energy of gamma-twisted BMN vacuum at single-wrapping orders of weak coupling expansion.

Keywords

AdS-CFT Correspondence Bethe Ansatz Integrable Field Theories Supersymmetric gauge theory 

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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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Vladimir Kazakov
    • 1
    • 2
  • Sébastien Leurent
    • 3
    Email author
  • Dmytro Volin
    • 4
    • 5
  1. 1.LPT, École Normale SuperieureParisFrance
  2. 2.Université Paris-VIParisFrance
  3. 3.Institut de Mathématiques de Bourgogne, UMR 5584 du CNRSUniv. Bourgogne Franche-ComtéDijonFrance
  4. 4.School of Mathematics, Trinity College DublinDublin 2Ireland
  5. 5.Nordita, KTH Royal Institute of Technology and Stockholm UniversityStockholmSweden

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