E. Sokatchev

Unconstrained N=2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace

A new approach to N=2 supersymmetry based on the concept of harmonic superspace is proposed and is used to give an unconstrained superfield geometric description of N=2 super Yang-Mills and supergravity theories as well as of matter N=2 hypermultiplets. The harmonic N=2 superspace has an independent coordinates, in addition to the usual ones, the isospinor harmonics ui+or- on the sphere SU(2)/U(1). The role of ui+or- is to relate the SU(2) group realised on the component fields to a U(1) group acting on the relevant superfields. Their introduction makes it possible to SU(2)-covariantise the notion of Grassmann analyticity. Crucial for the construction is the existence of an analytic subspace of the general harmonic N=2 superspace. The hypermultiplet superfields and the true prepotentials (pre-prepotentials) of N=2 super Yang-Mills and supergravity are unconstrained superfunctions over this analytic subspace. The pre-prepotentials have a clear geometric interpretation as gauge connections with respect to the internal SU(2)/U(1) directions. A radically new feature arises: the number of gauge and auxiliary degrees of freedom becomes infinite while the number of physical degrees of freedom remains finite. Other new results are the massive N=2 Yang-Mills theory and various off-shell self-interactions of hypermultiplets. The propagators for matter and Yang-Mills superfields are given.

Conformal properties of four-gluon planar amplitudes and Wilson loops

We present further evidence for a dual conformal symmetry in the four-gluon planar scattering amplitude in N=4 SYM. We show that all the momentum integrals appearing in the perturbative on-shell calculations up to four loops are dual to true conformal integrals, well defined off shell. Assuming that the complete off-shell amplitude has this dual conformal symmetry and using the basic properties of factorization of infrared divergences, we derive the special form of the finite remainder previously found at weak coupling and recently reproduced at strong coupling by AdS/CFT. We show that the same finite term appears in a weak coupling calculation of a Wilson loop whose contour consists of four light-like segments associated with the gluon momenta. We also demonstrate that, due to the special form of the finite remainder, the asymptotic Regge limit of the four-gluon amplitude coincides with the exact expression evaluated for arbitrary values of the Mandelstam variables.

On planar gluon amplitudes/Wilson loops duality

There is growing evidence that on-shell gluon scattering amplitudes in planar N=4 SYM theory are equivalent to Wilson loops evaluated over contours consisting of straight, light-like segments defined by the momenta of the external gluons. This equivalence was first suggested at strong coupling using the AdS/CFT correspondence and has since been verified at weak coupling to one loop in perturbation theory. Here we perform an explicit two-loop calculation of the Wilson loop dual to the four-gluon scattering amplitude and demonstrate that the relation holds beyond one loop. We also propose an anomalous conformal Ward identity which uniquely fixes the form of the finite part (up to an additive constant) of the Wilson loop dual to four- and five-gluon amplitudes, in complete agreement with the BDS conjecture for the multi-gluon MHV amplitudes

The hexagon Wilson loop and the BDS ansatz for the six-gluon amplitude

Abstract As a test of the gluon scattering amplitude/Wilson loop duality, we evaluate the hexagonal light-like Wilson loop at two loops in N = 4 super-Yang–Mills theory. We compare its finite part to the Bern–Dixon–Smirnov (BDS) conjecture for the finite part of the six-gluon amplitude. We find that the two expressions have the same behavior in the collinear limit, but they differ by a non-trivial function of the three (dual) conformally invariant variables. This implies that either the BDS conjecture or the gluon amplitude/Wilson loop duality fails for the six-gluon amplitude, starting from two loops. Our results are in qualitative agreement with the analysis of Alday and Maldacena of scattering amplitudes with infinitely many external gluons.

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

Harmonic supergraphs: Green functions

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

From correlation functions to scattering amplitudes

. 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

Partial non-renormalisation of the stress-tensor four-point function in N = 4 SYM and AdS/CFT

\mathcal{N} = 4

Harmonic supergraphs: Feynman rules and examples

super-Yang-Mills theory.

Four point functions in N=4 supersymmetric Yang-Mills theory at two loops

The quantisation procedure in the harmonic superspace approach is worked out. Harmonic distributions are introduced and are used to construct the analytic superspace delta functions and the Green functions for the hypermultiplet and the N=2 Yang-Mills superfields. The gauge fixing is described and the relevant Faddeev-Popov ghosts are defined. The corresponding BRST transformations are found. The harmonic superspace quantisation of the N=2 gauge theory turns out to be rather simple and has many parallels with that for the standard (N=0) Yang-Mills theory. In particular, no ghosts-for-ghosts are needed.