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arXiv · 1405.4857

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

Nikolay Gromov·Vladimir Kazakov·Sebastien Leurent·Dmytro Volin
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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.

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Nikolay Gromov, Vladimir Kazakov, Sebastien Leurent, Dmytro Volin. 2015-10-13. Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$. https://doi.org/10.1007/jhep09(2015)187

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