Abstract
I consider three-point functions of twist-one operators in ABJM at weak coupling. I compute the structure constant of correlators involving one twist-one un-protected operator and two protected ones for a few finite values of the spin, up to two-loop order. As an application I enforce a limit on the gauge group ranks, in which I relate the structure constant for three chiral primary operators to the expectation value of a supersymmetric Wilson loop. Such a relation is then used to perform a successful five-loop test on the matrix model conjectured to describe the supersymmetric Wilson loop.
Highlights
ABJM lacks any perturbative data on three-point functions at quantum level whatsoever, except for the computation of the two-loop structure constant of three protected operators of [7, 8]
The idea behind this connection lies in the existence of a class of diagrams in the perturbative expansion of the supersymmetric Wilson loop, which effectively contains a three-point function correlator of local length-two chiral primary operators constructed as an R-symmetry traceless combination of the scalar fields
Supersymmetric Wilson loops can be defined in the ABJM model [1, 14], which are in principle amenable of an exact computation via localization [32]
Summary
Supersymmetric Wilson loops can be defined in the ABJM model [1, 14], which are in principle amenable of an exact computation via localization [32] This program has been accomplished extensively for the 1/6 [33,34,35,36] and 1/2 [37] operators associated to a circular contour on the great circle of S3 [38,39,40]. Supersymmetry can be conserved, albeit in a reduced amount, moving away from the great circle [41] Among this class of operators a simple representative is the so-called latitude Wilson loop [12], which is named after its contour being a circle at a certain azimuthal angle from the equator of S3, which I dub Γn (n standing for potential multiple winding). Despite a number of perturbative checks [29, 44,45,46], (2.3) remains a conjecture and amenable of further tests, which is part of the purpose of this paper
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