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

TL;DR

This paper extends the duality between MHV amplitudes and correlation functions in N=4 SYM to non-MHV amplitudes, using super-correlators of stress-tensor multiplets at Born level, linking correlators to super-amplitudes at tree and loop levels.

Contribution

It generalizes the amplitude-correlator duality to non-MHV amplitudes using super-correlators and develops the superspace formalism for this duality in planar N=4 SYM.

Findings

Correlators at Born level reproduce super-amplitudes in the light-cone limit.

Loop corrections correspond to integrated Lagrangian insertions in correlators.

Explicit example provided for the n-point NMHV tree amplitude.

Abstract

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.