6533b855fe1ef96bd12b081b
RESEARCH PRODUCT
Quantum spectral curve for arbitrary state/operator in AdS$_5$/CFT$_4$
Dmytro VolinDmytro VolinSebastien LeurentNikolay GromovVladimir KazakovVladimir KazakovVladimir Kazakovsubject
PhysicsHigh Energy Physics - TheoryNuclear and High Energy Physics010308 nuclear & particles physicsOperator (physics)Spectrum (functional analysis)FOS: Physical sciencesMathematical Physics (math-ph)State (functional analysis)AdS-CFT Correspondence01 natural sciencesAdS/CFT correspondenceHigh Energy Physics - Theory (hep-th)MonodromyPhysical Sciences0103 physical sciencesFysikIntegrable Field TheoriesAnti-de Sitter space010306 general physicsFinite setQuantumMathematical PhysicsMathematical physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-09-01 |