Approaching the BFKL pomeron via integrable classical solutions

Abstract

We identify classical string solutions which directly give the classical part of the strong coupling pomeron intercept. The relevant solution is a close cousin of the GKP folded string, which is not surprising given the known relation with twist-2 operators. Our methods are applicable, however, also for nonzero conformal spin where we do not have a clear link with anomalous dimensions of a concrete class of operators. We analyze the BFKL folded string from the algebraic curve perspective and investigate its possible particle content.

Adjoint BFKL at finite coupling: a short-cut from the collinear limit

“…One similarity with ref. [59] is that for ν real and large enough the solution changes non-analytically. For us the transition occurs at θ = ±∞ where ν = ± πΓcusp 2 and eq.…”

“…A classical solution related to BFKL in the color-singlet sector (that is, the Pomeron with large Mellin moment ν ∼ √ λ) was described in ref. [59]. In that reference the case of real ν was considered, and the solutions are correspondingly complex.…”

“…It is interesting to ask what the solution of ref. [59], itself an analytic continuation of the GKP string, would look like for imaginary ν. In fact this was plotted already in fig.…”

BFKL spectrum of $$ \mathcal{N} $$ = 4: non-zero conformal spin

“…The other interesting limit of the intercept function besides the small coupling limit considered in the section 4 is the strong coupling one. For n = 0 case the intercept function in the strong coupling limit was analyzed in [41,[76][77][78] and then extended to the next orders by the QSC method in [21]. As we have already the numerical data for the intercept for the different values of conformal spin n, then using the numerical algorithm described in the section 3 and assuming that the coefficients are some simple rational numbers and extrapolating the high precision numerical data by the inverse powers of λ 1/2 we extract…”

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

“…One could either attempt a direct approach dealing with observables directly linked to the pomeron, or a more indirect approach which uses the very close links between BFKL and the anomalous dimensions of twist-2 operators about which we have currently quite detailed knowledge. In this paper we will pursue this latter approach, leaving the more direct approach to a forthcoming paper [7].…”