Revisiting instanton corrections to the Konishi multiplet

We revisit the calculation of instanton effects in correlation functions in ${\cal N}=4$ SYM involving the Konishi operator and operators of twist two. Previous studies revealed that the scaling dimensions and the OPE coefficients of these operators do not receive instanton corrections in the semiclassical approximation. We go beyond this approximation and demonstrate that, while operators belonging to the same ${\cal N}=4$ supermultiplet ought to have the same conformal data, the evaluation of quantum instanton corrections for one operator can be mapped into a semiclassical computation for another operator in the same supermultiplet. This observation allows us to compute explicitly the leading instanton correction to the scaling dimension of operators in the Konishi supermultiplet as well as to their structure constants in the OPE of two half-BPS scalar operators. We then use these results, together with crossing symmetry, to determine instanton corrections to scaling dimensions of twist-four operators with large spin.Comment: 25 pages; v2: minor changes, typos correcte

On near forward high energy scattering in QCD

We consider elastic quark-quark scattering at high energy and fixed transferred momentum. Performing factorization of soft gluon exchanges into Wilson lines vacuum expectation values and studying their properties, we find that the asymptotics of the scattering amplitude is controlled by the renormalization properties of the so called cross singularities of Wilson loops. Using this fact, we evaluate the scattering amplitude and show that its asymptotics is determined by the properties of the $2\times 2$ matrix of anomalous dimensions which appears after one renormalizes the cross singularities of Wilson loops. A generalization to the case of quark-antiquark and gluon-gluon elastic scattering is discussed.Comment: LaTeX style, 13 pages, 4 figures (included

Power Corrections and Nonlocal Operators

We discuss power corrections to infrared safe cross sections and event shapes, and identify a nonperturbative function that governs 1/Q corrections to these quantities.Comment: 4 pages, to appear in Proceedings of the Fifth International Workshop on Deep Inelastic Scattering and QC

Power corrections to event shapes and factorization

We study power corrections to the differential thrust, heavy mass and related event shape distributions in $e^+e^-$-annihilation, whose values, $e$, are proportional to jet masses in the two-jet limit, $e\to 0$. The factorization properties of these differential distributions imply that they may be written as convolutions of nonperturbative "shape" functions, describing the emission of soft quanta by the jets, and resummed perturbative cross sections. The infrared shape functions are different for different event shapes, and depend on a factorization scale, but are independent of the center-of-mass energy $Q$. They organize all power corrections of the form $1/(eQ)^n$, for arbitrary $n$, and carry information on a class of universal matrix elements of the energy-momentum tensor in QCD, directly related to the energy-energy correlations.Comment: 15 pages, LaTeX style, 1 figure embedded with epsf.st

The three-loop cusp anomalous dimension in QCD

We present the full analytic result for the three-loop angle-dependent cusp anomalous dimension in QCD. With this result, infrared divergences of planar scattering processes with massive particles can be predicted to that order. Moreover, we define a closely related quantity in terms of an effective coupling defined by the light-like cusp anomalous dimension. We find evidence that this quantity is universal for any gauge theory, and use this observation to predict the non-planar $n_{f}$-dependent terms of the four-loop cusp anomalous dimension.Comment: 5 pages, 2 figure

The nfn_{f} terms of the three-loop cusp anomalous dimension in QCD

In this talk we present the result for the $n_f$ dependent piece of the three-loop cusp anomalous dimension in QCD. Remarkably, it is parametrized by the same simple functions appearing in analogous anomalous dimensions in ${\mathcal N}=4$ SYM at one and two loops. We also compute all required master integrals using a recently proposed refinement of the differential equation method. The analytic results are expressed in terms of harmonic polylogarithms of uniform weight.Comment: 8 pages, 2 figures; v2: typo in eq. (4.4) fixed, 'three-loop' added to titl

From correlation functions to Wilson loops

We start with an n-point correlation function in a conformal gauge theory. We show that a special limit produces a polygonal Wilson loop with $n$ sides. The limit takes the $n$ points towards the vertices of a null polygonal Wilson loop such that successive distances $x^2_{i,i+1} \to 0$. This produces a fast moving particle that generates a "frame" for the Wilson loop. We explain in detail how the limit is approached, including some subtle effects from the propagation of a fast moving particle in the full interacting theory. We perform perturbative checks by doing explicit computations in N=4 super-Yang-Mills.Comment: 37 pages, 10 figures; typos corrected, references adde

The super-correlator/super-amplitude duality: Part I

We extend the recently discovered duality between MHV amplitudes and the light-cone limit of correlation functions of a particular type of local scalar operators to generic non-MHV amplitudes in planar N=4 SYM theory. We consider the natural generalization of the bosonic correlators to super-correlators of stress-tensor multiplets and show, in a number of examples, that their light-cone limit exactly reproduces the square of the matching super-amplitudes. Our correlators are computed at Born level. If all of their points form a light-like polygon, the correlator is dual to the tree-level amplitude. If a subset of points are not on the polygon but are integrated over, they become Lagrangian insertions generating the loop corrections to the correlator. In this case the duality with amplitudes holds at the level of the integrand. We build up the superspace formalism needed to formulate the duality and present the explicit example of the n-point NMHV tree amplitude as the dual of the lowest nilpotent level in the correlator.Comment: 56 page

More on the duality correlators/amplitudes

We continue the study of n-point correlation functions of half-BPS protected operators in N=4 super-Yang-Mills theory, in the limit where the positions of the adjacent operators become light-like separated. We compute the l-loop corrections by making l Lagrangian insertions. We argue that there exists a simple relation between the (n+l)-point tree-level correlator with l Lagrangian insertions and the integrand of the n-particle l-loop MHV scattering amplitude, as obtained by the recent momentum twistor construction of Arkani-Hamed et al. We present several examples of this new duality, at one and two loops.Comment: 14 pages Latex, 1 figur