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.

Abstract:We elaborate on a non-perturbative formulation of scattering amplitudes/null polygonal Wilson loops in planar N = 4 Super-Yang-Mills theory. It allows one to compute a precise IR finite ratio of scattering amplitudes that captures all the conformally invariant data of interest. Our construction is based on a decomposition of the dual Wilson loops into elementary building blocks named pentagon transitions. This discussion expands on a previous letter of the authors where these transitions were introduced and analyzed for the so-called gluonic excitations. In this paper we revisit these transitions and extend the analysis to the sector of scalar excitations. We restrict ourselves to the single particle transitions and bootstrap their finite coupling expressions using a set of axioms. Besides these considerations, the main focus of the paper is on the extraction of perturbative data from scattering amplitudes at weak coupling and its comparison against the proposed pentagon transitions. We present several tests for both the hexagon and heptagon (MHV and NMHV) amplitudes up to two-and three-loop orders. In attached notebooks we provide explicit higher-loop predictions obtained from our method.

We consider light-like Wilson loops with hexagonal geometry in the planar limit of N = 4 Super-Yang-Mills theory. Within the Operator-Product-Expansion framework these loops receive contributions from all states that can propagate on top of the colour flux tube sourced by any two opposite edges of the loops. Of particular interest are the two-particle contributions. They comprise virtual effects like the propagation of a pair of scalars, fermions, and gluons, on top of the flux tube. Each one of them is thoroughly discussed in this paper. Our main result is the prediction of all the twist-2 corrections to the expansion of the dual 6-gluons MHV amplitude in the near-collinear limit at finite coupling. At weak coupling, our result was recently used by Dixon, Drummond, Duhr and Pennington to predict the full amplitude at four loops. At strong coupling, it allows us to make contact with the classical string description and to recover the (previously elusive) AdS 3 mode from the continuum of two-fermion states. More generally, the two-particle contributions serve as an exemplar for all the multi-particle corrections.

We construct an analytical solution to the integral equation which is believed to describe logarithmic growth of the anomalous dimensions of high spin operators in planar N = 4 super Yang-Mills theory and use it to determine the strong coupling expansion of the cusp anomalous dimension.

We analyze the pentagon transitions involving arbitrarily many flux-tube gluonic excitations and bound states thereof in planar N = 4 Super-Yang-Mills theory. We derive all-loop expressions for all these transitions by factorization and fusion of the elementary transitions for the lightest gluonic excitations conjectured in a previous paper. We apply the proposals so obtained to the computation of MHV and NMHV scattering amplitudes at any loop order and find perfect agreement with available perturbative data up to four loops.

We analyze the spectrum of excitations around the Gubser-Klebanov-Polyakov (GKP) rotating string in the long string limit and construct a parametric representation for their dispersion relations at any value of the string tension. On the gauge theory side of the AdS/CFT correspondence, i.e., in the planar N = 4 Super-Yang-Mills theory, the problem is equivalent to finding the spectrum of scaling dimensions of large spin, single-trace operators. Their scaling dimensions are obtained from the analysis of the Beisert-Staudacher asymptotic Bethe ansatz equations, which are believed to solve the spectral problem of the planar gauge theory. We examine the resulting dispersion relations in various kinematical regimes, both at weak and strong coupling, and detail the matching with the Frolov-Tseytlin spectrum of transverse fluctuations of the long GKP string. At a more dynamical level, we identify the mechanism for the restoration of the SO(6) symmetry, initially broken by the choice of the Berenstein-Maldacena-Nastase vacuum in the Bethe ansatz solution to the mixing problem.dedicated to the memory of Jacques Basso

Anomalous dimensions of Wilson operators with large Lorentz spin scale logarithmically with the spin. Recent multi-loop QCD calculations of twist-two anomalous dimensions revealed the existence of interesting structure of the subleading corrections suppressed by powers of the Lorentz spin. We argue that this structure is a manifestation of the `self-tuning' property of the multi-loop anomalous dimensions - in a conformal gauge theory, the anomalous dimension of Wilson operators is a function of their conformal spin which is modified in higher loops by an amount proportional to the anomalous dimension. Making use of the parity property of this function and incorporating the beta-function contribution, we demonstrate the existence of (infinite number of) relations between subleading corrections to the twist-two anomalous dimensions in QCD and its supersymmetric extensions. They imply that the subleading corrections to the anomalous dimensions suppressed by odd powers of the conformal spin can be expressed in terms of the lower-loops corrections suppressed by smaller even powers of the spin. We show that these relations hold true in QCD to all loops in the large beta0 limit. In the N=4 SYM theory, we employ the AdS/CFT correspondence to argue that the same relations survive in the strong coupling regime for higher-twist scalar operators dual to a folded string rotating on the AdS3xS1.Comment: 29 pages; v2: minor changes, references added; v3: eqs.(3.25) and (3.26) correcte

In this letter we consider the collinear limit of gluon scattering amplitudes in planar N = 4 SYM theory at strong coupling. We argue that in this limit scattering amplitudes map into correlators of twist fields in the two dimensional non-linear O(6) sigma model, similar to those appearing in recent studies of entanglement entropy. We provide evidence for this assertion by combining the intuition springing from the string worldsheet picture and the predictions coming from the OPE series. One of the main implications of these considerations is that scattering amplitudes receive equally important contributions at strong coupling from both the minimal string area and its fluctuations in the sphere.