Quantum spectral curve for arbitrary state/operator in \(\mathrm{AdS}_{5}/\mathrm{CFT}_{4}\)
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Publication:2635896
DOI10.1007/JHEP09(2015)187zbMATH Open1388.81214arXiv1405.4857OpenAlexW3099621541WikidataQ62049159 ScholiaQ62049159MaRDI QIDQ2635896
Author name not available (Why is that?)
Publication date: 31 May 2018
Published in: (Search for Journal in Brave)
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.
Full work available at URL: https://arxiv.org/abs/1405.4857
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