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 RiemannHilbert 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 TBAlike 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 Qsystem — a finite set of Baxterlike Qfunctions. 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 Ysystem/TBA, or FiNLIE). We use the knowledge of this underlying Qsystem to demonstrate how the classical finite gap solutions and the asymptotic Bethe ansatz emerge from our formalism in appropriate limits.
 Publication:

Journal of High Energy Physics
 Pub Date:
 September 2015
 DOI:
 10.1007/JHEP09(2015)187
 arXiv:
 arXiv:1405.4857
 Bibcode:
 2015JHEP...09..187G
 Keywords:

 AdSCFT Correspondence;
 Integrable Field Theories;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 96 pages, 15 figures