From Correlators to Wilson Loops in Chern-Simons Matter Theories

TL;DR

This paper explores the relationship between n-point correlation functions and Wilson loops in three-dimensional supersymmetric Chern-Simons matter theories, revealing a simple connection in the light-like limit and confirming previous results.

Contribution

It demonstrates that in certain supersymmetric Chern-Simons theories, the light-like limit of correlation functions matches Wilson loops, with an explicit analytical evaluation showing a vanishing result.

Findings

Correlation functions match Wilson loops in the light-like limit

Analytical evaluation of integrals yields a zero result

Results agree with previous findings for Wilson loops

Abstract

We study n-point correlation functions for chiral primary operators in three dimensional supersymmetric Chern-Simons matter theories. Our analysis is carried on in N=2 superspace and covers N=2,3 supersymmetric CFT's, the N=6 ABJM and the N=8 BLG models. In the limit where the positions of adjacent operators become light-like, we find that the one-loop n-point correlator divided by its tree level expression coincides with a light-like n-polygon Wilson loop. Remarkably, the result can be simply expressed as a linear combination of five dimensional two-mass easy boxes. We manage to evaluate the integrals analytically and find a vanishing result, in agreement with previous findings for Wilson loops.