Supersymmetric Wilson loops in super-Chern–Simons-matter theory

Abstract

We study supersymmetric Wilson loop operators in ABJM theory from both sides of the AdS 4 /CF T 3 correspondence. We first construct some supersymmetric Wilson loops. The perturbative computations are performed in the field theory side at the first two orders. A fundamental string solution ending on a circular loop is also studied.

BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis

“…Their evaluation is straightforward and parallels the wellknown computation of the 1/6−BPS Wilson loop [23][24][25]. In dimensional regularization (then assuming framing zero), the only…”

“…Perturbative results for 1/6−BPS Wilson loops [24,25,29,30] on the maximal circle have been proved to match the exact prediction obtained by using localization techniques [31]. At variance with N = 4 SYM [32], the corresponding matrix model is no longer gaussian due to non-trivial contributions from the vector and the matter multiplets.…”

“…It naturally includes a non-trivial coupling to the scalars of the form M I J (τ )C IC J , governed by a matrix which is locally defined along the path. When M is constant, M = diag(1, 1, −1, −1) and the path is chosen to be a maximal circle on S 2 , we obtain the well studied 1/6−BPS Wilson loop W 1/6 [23][24][25]. Adding local couplings to the fermions allows to generalize the Wilson operator to the holonomy of a superconnection of the U(N |M ) supergroup, leading to an enhanced 1/2−BPS operator W 1/2 [26] (see also [27] for an alternative derivation and [28] for previous attempts).…”

“…The former features the oneloop correction to the gauge propagator, which is non-vanishing thanks to matter fields running inside the loop, whereas the latter originates from the contractions of the scalar bilinears and is controlled by the matrix M ( M in the bosonic case). Such pieces can be conveniently combined into an effective contribution [23][24][25]. For the upper-left part of the superconnection it reads…”

Wilson loops in N $$ \mathcal{N} $$ = 6 superspace for ABJM theory

“…However, this is not the only option; one could instead consider the supertrace (see the discussions in refs. [52][53][54][55][56][57][58]). We will restrict to the planar limit, where N → ∞, M → ∞, k → ∞ such that the ratios N k and M k are constant.…”