Nikolay Gromov

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection, we present an overview of the achievements and the status of this subject as of the year 2010.

Exact Spectrum of Anomalous Dimensions of Planar N=4 Supersymmetric Yang-Mills Theory

Nikolay Gromov, Vladimir Kazakov, and Pedro Vieira DESY Theory, Hamburg, Germany & II. Institut für Theoretische Physik Universität, Hamburg, Germany & St.Petersburg INP, St.Petersburg, Russia Ecole Normale Superieure, LPT, 75231 Paris CEDEX-5, France & l’Université Paris-VI, Paris, France; Max-Planck-Institut für Gravitationphysik, Albert-Einstein-Institut, 14476 Potsdam, Germany & Centro de F́ısica do Porto, Faculdade de Ciências da Universidade do Porto, 4169-007 Porto, Portugal

Tailoring three-point functions and integrability

We use integrability techniques to compute structure constants in

Exact Spectrum of Planar N=4 Supersymmetric Yang-Mills Theory: Konishi Dimension at Any Coupling

\mathcal{N} = 4

Quantum spectral curve for planar N=4 super-Yang-Mills theory.

SYM to leading order at weak coupling and to leading order in the planar expansion. Three closed spin chains, which represent the single trace gauge-invariant operators in

Exact AdS/CFT spectrum: Konishi dimension at any coupling

\mathcal{N} = 4

The AdS(5)xS(5) superstring quantum spectrum from the algebraic curve

SYM, are cut into six open chains which are then sewed back together into some nice pants, the three-point function. The algebraic and coordinate Bethe ansatz tools necessary for this task are reviewed. Our results hold for scalar single trace operators of arbitrary size. Finally, we discuss the classical limit of our results, anticipating some predictions for quasi-classical string correlators in terms of algebraic curves.

Complete 1-loop test of AdS/CFT

We compute the full dimension of Konishi operator in planar N=4 SYM theory it for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A.Kozak.

Tailoring three-point functions and integrability II. Weak/strong coupling match

We present a new formalism, alternative to the old TBA-like approach, for solution of the spectral problem of planar N = 4 SYM. It takes a concise form of a non-linear matrix Riemann-Hilbert problem in terms of a few Q-functions. We demonstrate the formalism for two types of observables - local operators at weak coupling and cusped Wilson lines in a near BPS limit.

Quantum spectral curve for arbitrary state/operator in AdS5/CFT4

We compute the full dimension of Konishi operator in planar N=4 SYM theory it for a wide range of couplings, from weak to strong coupling regime, and predict the subleading terms in its strong coupling asymptotics. For this purpose we solve numerically the integral form of the AdS/CFT Y-system equations for the exact energies of excited states proposed by us and A.Kozak.