Review of AdS/CFT Integrability, Chapter III.7: Hirota Dynamics for Quantum Integrability

Abstract

We review recent applications of the integrable discrete Hirota dynamics (Y-system) in the context of calculation of the planar AdS/CFT spectrum. We start from the description of solution of Hirota equations by the Backlund method where the requirement of analyticity results in the nested Bethe ansatz equations. Then we discuss applications of the Hirota dynamics for the analysis of the asymptotic limit of long operators in the AdS/CFT Y-system.

24 pages, see also overview article arXiv:1012.3982, v2: references to other chapters updated

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Cited by in corpus (28)

• Ballistic transport in the one-dimensional Hubbard model: the hydrodynamic approach
• The quark anti-quark potential and the cusp anomalous dimension from a TBA equation
• Super-diffusion in one-dimensional quantum lattice models
• Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$
• Review of AdS/CFT Integrability, Chapter IV.3: N=6 Chern-Simons and Strings on AdS4xCP3
• Solving the AdS/CFT Y-system
• Superstrings in AdS(2)xS(2)xT(6)
• Wronskian Solution for AdS/CFT Y-system
• Oscillator Construction of su(n|m) Q-Operators
• Dual Separated Variables and Scalar Products
• Non-conformality of gamma_i-deformed N=4 SYM theory
• N=4 SYM structure constants as determinants
• Yangians, S-matrices and AdS/CFT
• Separation of variables and scalar products at any rank
• Wronskian solutions of the T, Q and Y-systems related to infinite dimensional unitarizable modules of the general linear superalgebra gl(M|N)
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• The complete one-loop dilatation operator of planar real beta-deformed N=4 SYM theory
• Review of AdS/CFT Integrability, Chapter III.1: Bethe Ansätze and the R-Matrix Formalism
• Colour-Twist Operators I: Spectrum and Wave Functions
• Quantum Spectral Curve of $\gamma$-twisted $\mathcal{N}=4$ SYM theory and fishnet CFT
• Y-system for Y=0 brane in planar AdS/CFT
• Review of AdS/CFT Integrability, Chapter II.2: Quantum Strings in AdS5xS5
• Wrapping corrections for long range spin chains
• Spectral curve for open strings attached to the Y=0 brane
• Wrapping corrections, reciprocity and BFKL beyond the sl(2) subsector in N=4 SYM
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• Spectral curve for gamma-deformed AdS/CFT
• Deforming integrable models of AdS${}_3$ strings