Quantum spectral curve for arbitrary state/operator in AdS${}_5$/CFT${}_4$

Abstract

We give a derivation of quantum spectral curve (QSC) - a finite set of Riemann-Hilbert equations for exact spectrum of planar N=4 SYM theory proposed in our recent paper Phys.Rev.Lett. 112 (2014). We also generalize this construction to all local single trace operators of the theory, in contrast to the TBA-like approaches worked out only for a limited class of states. We reveal a rich algebraic and analytic structure of the QSC in terms of a so called Q-system -- a finite set of Baxter-like Q-functions. This new point of view on the finite size spectral problem is shown to be completely compatible, though in a far from trivial way, with already known exact equations (analytic Y-system/TBA, or FiNLIE). We use the knowledge of this underlying Q-system to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.

96 pages, 15 figures; Some mathematica examples added in v2; Published version is v3

References in corpus (12)

• Thermodynamic Bethe Ansatz for the AdS_5 x S^5 Mirror Model
• Supersymmetric Bethe Ansatz and Baxter Equations from Discrete Hirota Dynamics
• The Quantum Spectral Curve of the ABJM theory
• On the exact spectrum and mirror duality of the (AdS_5 x S^5)_eta superstring
• All-loop worldsheet S matrix for AdS_3 x S^3 x T^4
• Complete 1-loop test of AdS/CFT
• Exact Slope and Interpolating Functions in ABJM Theory
• Wronskian Solution for AdS/CFT Y-system
• Quantum Spectral Curve at Work: From Small Spin to Strong Coupling in N=4 SYM
• From Characters to Quantum (Super)Spin Chains via Fusion
• Six-loop Konishi anomalous dimension from the Y-system
• The spectrum of tachyons in AdS/CFT

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