ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes encoded in a permutation-symmetric generating function of planar f-graphs.
From Correlators to Wilson Loops in Chern-Simons Matter Theories
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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.
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Loops and legs: ABJM amplitudes from $f$-graphs
ABJM amplitudes of arbitrary multiplicity and loop order can be reconstructed from squared amplitudes encoded in a permutation-symmetric generating function of planar f-graphs.