Algebraic Curve for a Cusped Wilson Line

We consider the classical limit of the recently obtained exact result for the anomalous dimension of a cusped Wilson line with the insertion of an operator with L units of R-charge at the cusp in planar N=4 SYM. The classical limit requires taking both the 't Hooft coupling and L to infinity. Since the formula for the cusp anomalous dimension involves determinants of size proportional to L, the classical limit requires a matrix model reformulation of the result. We construct such matrix model-like representation and find corresponding classical algebraic curve. Using this we derive the classical value of the cusp anomalous dimension and the 1-loop correction to it. We check our results against the energy of the classical solution and numerically by extrapolating from the quantum regime of finite L.Comment: 15 pages, 2 figure

BFKL Spectrum of N=4 SYM: non-Zero Conformal Spin

We developed a general non-perturbative framework for the BFKL spectrum of planar N=4 SYM, based on the Quantum Spectral Curve (QSC). It allows one to study the spectrum in the whole generality, extending previously known methods to arbitrary values of conformal spin $n$. We show how to apply our approach to reproduce all known perturbative results for the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue and get new predictions. In particular, we re-derived the Faddeev-Korchemsky Baxter equation for the Lipatov spin chain with non-zero conformal spin reproducing the corresponding BFKL kernel eigenvalue. We also get new non-perturbative analytic results for the Pomeron eigenvalue in the vicinity of $|n|=1,\;\Delta=0$ point and we obtained an explicit formula for the BFKL intercept function for arbitrary conformal spin up to the 3-loop order in the small coupling expansion and partial result at the 4-loop order. In addition, we implemented the numerical algorithm of arXiv:1504.06640 as an auxiliary file to this arXiv submission. From the numerical result we managed to deduce an analytic formula for the strong coupling expansion of the intercept function for arbitrary conformal spin.Comment: 70 pages, 5 figures, 1 txt, 2 nb and 2 mx files; v2: references added, typos fixed and nb file with Mathematica stylesheet attached; v3: more typos fixed; v4: the text edited according to the report of the refere

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

We 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 gamma-deformed case and discuss our results in the framework of the novel ${\bf P}\mu$-formulation of the spectral problem.Comment: 39 pages, 4 figures; v2: minor corrections, references added; v3: typos fixed, references updated; v4: typos fixe

NNLO BFKL Pomeron eigenvalue in N=4 SYM

We obtain an analytical expression for the Next-to-Next-to-Leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar SYM N=4 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.Comment: 6 pages; v2: typos fixed, references and supplementary Mathematica files adde

Prospects of supervising service development as the tool of input quality control

Supervising provides a foothold in the Russian Federation domestic market of oilfield services. Despite the rapid growth of supervising services market, there is still a definite demand in developing this domain. The authors consider the implementation of supervising in Russian oil and gas industry sector, as well as the possible execution paths of its improvement and development