Grigory Sizov

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.

Exact Slope and Interpolating Functions in N=6 Supersymmetric Chern-Simons Theory

Using the Quantum Spectral Curve approach we compute exactly an observable (called slope function) in the planar ABJM theory in terms of an unknown interpolating function h(λ) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semiclassical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(λ) to all orders. By comparing the structure of our result with that of an exact localization based calculation for a similar observable we conjecture an exact expression for h(λ).

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

We obtain an analytical expression for the Next-to-Next-to-Leading order of the Balitsky-FadinKuraev-Lipatov (BFKL) Pomeron eigenvalue in planar N = 4 SYM using Quantum Spectral Curve (QSC) integrability based method. The result is verified with more than 60 digits precision using the numerical method developed by us in a previous paper. As a byproduct we developed a general analytic method of solving the QSC perturbatively.We obtain an analytical expression for the next-to-next-to-leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar N=4 SYM using quantum spectral curve (QSC) integrability-based method. The result is verified with more than 60-digit precision using the numerical method developed by us in a previous paper [N. Gromov, F. Levkovich-Maslyuk, and G. Sizov, arXiv:1504.06640]. As a by-product, we developed a general analytic method of solving the QSC perturbatively.

Exact slope and interpolating functions in ABJM theoryy

Using the Quantum Spectral Curve approach we compute exactly an observable (called slope function) in the planar ABJM theory in terms of an unknown interpolating function h(\lambda) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semi-classical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(\lambda) to all orders. By comparing the structure of our result with that of an exact localization-based calculation for a similar observable in JHEP 1006 (2010) 011 we conjecture an exact expression for h(\lambda).

Quantum Spectral Curve and the Numerical Solution of the Spectral Problem in AdS 5 /CF T 4

A bstractWe developed an efficient numerical algorithm for computing the spectrum of anomalous dimensions of the planar N

New construction of eigenstates and separation of variables for SU(N) quantum spin chains

\mathcal{N}

CSW-like expansion for Einstein gravity

= 4 Super-Yang-Mills at finite coupling. The method is based on the Quantum Spectral Curve formalism. In contrast to Thermodynamic Bethe Ansatz, worked out only for some very special operators, this method is applicable for generic states/operators and is much faster and more precise due to its Q-quadratic convergence rate.To demonstrate the method we evaluate the dimensions Δ of twist operators in sl2