Twist-two operators and the BFKL regime — nonstandard solutions of the Baxter equation

We explore a direct connection between the collinear limit and the multiRegge limit for scattering amplitudes in the N = 4 super Yang-Mills theory. Starting with the collinear expansion for the six-gluon amplitude in the Euclidean kinematic region, we perform an analytic continuation term by term to the so-called Mandelstam region. We find that the result coincides with the collinear expansion of the analytically continued amplitude. We then take the multi-Regge limit, and conjecture that the final result precisely reproduces the one from the BFKL approach. Combining this procedure with the OPE for null polygonal Wilson loops, we explicitly compute the leading contribution in the "collinear-Regge" limit up to five loops. Our results agree with all the known results up to four loops. At five-loop, our results up to the next-to-next-to-leading logarithmic approximation (NNLLA) also reproduce the known results, and for the N 3 LLA and the N 4 LLA give non-trivial predictions. We further present an all-loop prediction for the imaginary part of the next-to-double-leading logarithmic approximation. Our procedure has a possibility of an interpolation from weak to strong coupling in the multi-Regge limit with the help of the OPE.

Section: Discussionmentioning

confidence: 99%

Wilson loop OPE, analytic continuation and multi-Regge limit

Hatsuda¹

2014

“…This connection will most likely involve some kind of analytic continuation, perhaps along the lines of ref. [141].…”

Section: Jhep05(2015)093mentioning

confidence: 99%

When does the gluon reggeize?

Caron-Huot

2015

137

346

Abstract:We propose the eikonal approximation as a simple and reliable tool to analyze relativistic high-energy processes, provided that the necessary subtleties are accounted for. An important subtlety is the need to include eikonal phases for a rapidity-dependent collection of particles, as embodied by the Balitsky-JIMWLK rapidity evolution equation. In the first part of this paper, we review how the phenomenon of gluon reggeization and the BFKL equations can be understood simply (but not too simply) in the eikonal approach. We also work out some previously overlooked implications of BFKL dynamics, including the observation that starting from four loops it is incompatible with a recent conjecture regarding the structure of infrared divergences. In the second part of this paper, we propose that in the strict planar limit the theory can be developed to all orders in the coupling with no reference at all to the concept of "reggeized gluon." Rather, one can work directly with a finite, process-dependent, number of Wilson lines. We demonstrate consistency of this proposal by an exact computation in N=4 super Yang-Mills, which shows that in processes mediated with two Wilson lines the reggeized gluon appears in the weak coupling limit as a resonance whose width is proportional to the coupling. We also provide a precise operator definition of Lipatov's integrable spin chain, which is manifestly integrable at any value of the coupling as a result of the duality between scattering amplitudes and Wilson loops in this theory.

“…Thus we formulate the "minimal" prescription for analytic continuation of Q-system to non-integer S: e 2π|u| asymptotic has to be allowed in ω 24 . This prescription was tested thoroughly on a variety of examples [31,32,15,12,30], but it would be interesting to derive it rigorously and generalize it to states outside of the sl(2) sector. Of course, one can also consider adding exponents to more than one component of ω ij : in this case the solution will not be unique.…”

Section: Modification Of the Algorithm For Non-integer Spinmentioning

confidence: 99%

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

Gromov

Levkovich-Maslyuk

Sizov

2016

162

Abstract:We developed an efficient numerical algorithm for computing the spectrum of anomalous dimensions of the planar N = 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 ∆ of twist operators in sl(2) sector directly for any value of the spin S including non-integer values. In particular, we compute the BFKL pomeron intercept in a wide range of the 't Hooft coupling constant with up to 20 significant figures precision, confirming two previously known from the perturbation theory orders and giving prediction for several new coefficients. Furthermore, we explore numerically a rich branch cut structure for complexified spin S.