Correlation functions, null polygonal Wilson loops, and local operators

TL;DR

This paper establishes a twistor space approach to relate correlation functions of local operators in N=4 super-Yang-Mills theory to null polygonal Wilson loops, providing recursion relations and exploring strong coupling challenges.

Contribution

It proves the equivalence between certain correlation functions and Wilson loops in twistor space, confirming recent conjectures and extending the analysis to multiple operators.

Findings

Correlation functions relate to null polygonal Wilson loops in twistor space.

A BCFW-like recursion relation for these correlators is derived.

Analysis of correlators with multiple operators reveals strong coupling difficulties.

Abstract

We consider the ratio of the correlation function of n+1 local operators over the correlator of the first n of these operators in planar N=4 super-Yang-Mills theory, and consider the limit where the first n operators become pairwise null separated. By studying the problem in twistor space, we prove that this is equivalent to the correlator of a n-cusp null polygonal Wilson loop with the remaining operator in general position, normalized by the expectation value of the Wilson loop itself, as recently conjectured by Alday, Buchbinder and Tseytlin. Twistor methods also provide a BCFW-like recursion relation for such correlators. Finally, we study the natural extension where n operators become pairwise null separated with k operators in general position. As an example, we perform an analysis of the resulting correlator for k=2 and discuss some of the difficulties associated to fixing the correlator completely in the strong coupling regime.