Spacetime and Flux TubeS-Matrices at Finite Coupling forN=4Supersymmetric Yang-Mills Theory

Abstract

We propose a nonperturbative formulation of planar scattering amplitudes in N=4 supersymmetric Yang-Mills theory, or, equivalently, polygonal Wilson loops. The construction is based on the operator product expansion approach and introduces a new decomposition of the Wilson loop in terms of fundamental building blocks named pentagon transitions. These transitions satisfy a simple relation to the worldsheet S matrix on top of the so-called Gubser-Klebanov-Polyakov vacuum which allows us to bootstrap them at any value of the coupling. In this Letter we present a subsector of the full solution which we call the gluonic part. We match our results with both weak and strong coupling data available in the literature.

Bootstrapping an NMHV amplitude through three loops

“…We were then able to fix those parameters with near-collinear data obtained from the work of Basso, Sever and Vieira [41]. The first-order T 1 correction in the near-collinear limit, from single flux excitations [42], was sufficient to fix all but two parameters in our ansatz.…”

“…[27], only the leading-discontinuity terms in the OPE were available [39]. Now, thanks to the work of BSV [41][42][43][44], who have used integrability to determine the OPE expansion exactly in the coupling, we have access to enough data to fix not only the two-loop, but also the three-loop six-point NMHV ratio function, without resorting to evaluating any loop integrals. The starting ansatz at two loops involves 50 parity-even weight-four hexagon functions for V (2) , and 2 parity-odd ones forṼ (2) .…”

“…[41]. It is a bit more complicated, but is still expressible in terms of the function ψ(x) = d ln Γ(x)/dx and its derivatives, as well as tanh πu.…”

“…These states have integrable 1 + 1 dimensional scattering matrices. In the past year or so, Basso, Sever and Vieira (BSV) have shown that the OPE is governed by "pentagon transitions", which they argue can be expressed in terms of the integrable S matrices [41] to all orders in the 't Hooft coupling. BSV have worked out the consequences of this picture in increasingly great detail [42][43][44].…”

“…In general, this limit may be expressed via a permutation of a map between the cross ratios (u, v, w) and the variables JHEP10(2014)065 (F, S, T ) ≡ (e iφ , e σ , e −τ ) defined in ref. [41]:…”