Gregory P. Korchemsky

Review of AdS/CFT Integrability: An Overview

This is the introductory chapter of a review collection on integrability in the context of the AdS/CFT correspondence. In the collection, we present an overview of the achievements and the status of this subject as of the year 2010.

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

From correlation functions to scattering amplitudes

x_{i,i + 1}^2 \to 0

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

. This produces a fast moving particle that generates a “frame” for the Wilson loop. We explainin 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

The Sudakov form factor in QCD

\mathcal{N} = 4

Bootstrapping correlation functions in N=4 SYM

super-Yang-Mills theory.

More on the duality correlators/amplitudes

A bstractWe study the correlation functions of half-BPS protected operators in

Are scattering amplitudes dual to super Wilson loops

\mathcal{N} = {4}

Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM

super-Yang-Mills theory, in the limit where the positions of adjacent operators become light-like separated. We compute the loop corrections by means of Lagrangian insertions. The divergences resulting from the light-cone limit are regularized by changing the dimension of the integration measure over the insertion points. Switching from coordinates to dual momenta, we show that the logarithm of the correlation function is identical with twice the logarithm of the matching MHV gluon scattering amplitude. We present a number of examples of this new relation, at one and two loops.

Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM

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 nonMHV 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. Unité de Recherche Associée au CNRS URA 2306 Laboratoire d’Annecy-le-Vieux de Physique Théorique, UMR 5108