Fedor Levkovich-Maslyuk

Y-system, TBA and Quasi-Classical Strings in AdS 4 × CP3

We study the exact spectrum of the AdS4/CFT3 duality put forward by Aharony, Bergman, Jafferis and Maldacena (ABJM). We derive thermodynamic Bethe ansatz (TBA) equations for the planar ABJM theory, starting from “mirror” asymptotic Bethe equations which we conjecture. We also propose generalization of the TBA equations for excited states. The recently proposed Y-system is completely consistent with the TBA equations for a large subsector of the theory, but should be modified in general. We find the general asymptotic infinite length solution of the Y-system, and also several solutions to all wrapping orders in the strong coupling scaling limit. To make a comparison with results obtained from string theory, we assume that the all-loop Bethe ansatz of N.G. and P. Vieira is the valid worldsheet theory description in the asymptotic regime. In this case we find complete agreement, to all orders in wrappings, between the solution of our Y-system and generic quasi-classical string spectrum in AdS3 × S1.

Quantum corrections to spinning superstrings in AdS 3 × S 3 × M 4 : determining the dressing phase

A bstractWe study the leading quantum string correction to the dressing phase in the asymptotic Bethe Ansatz system for superstring in AdS3 × S3 × T4 supported by RR flux. We find that the phase should be different from the phase appearing in the AdS5 × S5 case. We use the simplest example of a rigid circular string with two equal spins in S3 and also consider the general approach based on the algebraic curve description. We also discuss the case of the AdS3 × S3 × S3 × S1 theory and find the dependence of the 1-loop correction to the effective string tension function h(λ) (expected to enter the magnon dispersion relation) on the parameter α related to the ratio of the two 3-sphere radii. This correction vanishes in the AdS3 × S3 × T4 case.

Y-system and beta-deformed N=4 Super-Yang-Mills

We show how the perturbation theory results recently obtained by F Fiamberti, A Santambrogio, C Sieg and D Zanon for operator anomalous dimensions of β-deformed super-Yang–Mills theory can be reproduced from the AdS5/CFT4 Y-system proposed by NG, V Kazakov and P Vieira. To do this, we obtain the general twisted asymptotic solution of this Y-system of functional equations. We show that existence of an additional parameter β in the deformed theory allows us to extract rich information about the perturbation theory integrals directly from the Y-system. Using this method we found a simple generating function for a broad class of such integrals.

Analytic Solution of Bremsstrahlung TBA II: Turning on the Sphere Angle

A bstractWe find an exact analytical solution of the Y-system describing a cusped Wilson line in the planar limit of N=4 SYM. Our explicit solution describes anomalous dimensions of this family of observables for any value of the ‘t Hooft coupling and arbitrary R-charge L of the local operator inserted on the cusp in a near-BPS limit.Our finding generalizes the previous results of one of the authors & Sever and passes several nontrivial tests. First, for a particular case L = 0 we reproduce the predictions of localization techniques. Second, we show that in the classical limit our result perfectly reproduces the existing prediction from classical string theory. In addition, we made a comparison with all existing weak coupling results and we found that our result interpolates smoothly between these two very different regimes of AdS/CFT. As a byproduct we found a generalization of the essential parts of the FiNLIE construction for the γ-deformed case and discuss our results in the framework of the novel Pμ-formulation of the spectral problem.

Quark-anti-quark potential in

A bstractWe construct a closed system of equations describing the quark-anti-quark potential at any coupling in planar N

4 SYM

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Quantum Spectral Curve for a cusped Wilson line in N=4 SYM

= 4 supersymmetric Yang-Mills theory. It is based on the Quantum Spectral Curve method supplemented with a novel type of asymptotics. We present a high precision numerical solution reproducing the classical and one-loop string predictions very accurately. We also analytically compute the first 7 nontrivial orders of the weak coupling expansion.Moreover, we study analytically the generalized quark-anti-quark potential in the limit of large imaginary twist to all orders in perturbation theory. We demonstrate how the QSC reduces in this case to a one-dimensional Schrodinger equation. In the process we establish a link between the Q-functions and the solution of the Bethe-Salpeter equation.

Pomeron Eigenvalue at Three Loops in N=4 Supersymmetric Yang-Mills Theory.

We show how the perturbation theory results recently obtained by F Fiamberti, A Santambrogio, C Sieg and D Zanon for operator anomalous dimensions of β-deformed super-Yang–Mills theory can be reproduced from the AdS5/CFT4 Y-system proposed by NG, V Kazakov and P Vieira. To do this, we obtain the general twisted asymptotic solution of this Y-system of functional equations. We show that existence of an additional parameter β in the deformed theory allows us to extract rich information about the perturbation theory integrals directly from the Y-system. Using this method we found a simple generating function for a broad class of such integrals.