Abstract
We construct the Wilson loop operator of \( \mathcal{N} \) = 6 super Chern-Simons-matter which is invariant under half of the supercharges of the theory and is dual to the simplest macroscopic open string in AdS 4 ×ℂℙ3. The Wilson loop couples, in addition to the gauge and scalar fields of the theory, also to the fermions in the bi-fundamental representation of the U(N) × U(M) gauge group. These ingredients are naturally combined into a superconnection whose holonomy gives the Wilson loop, which can be defined for any representation of the supergroup U(N|M). Explicit expressions for loops supported along an infinite straight line and along a circle are presented. Using the localization calculation of Kapustin et al. we show that the circular loop is computed by a supermatrix model and discuss the connection to pure Chern-Simons theory with supergroup U(N|M).
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Drukker, N., Trancanelli, D. A supermatrix model for \( \mathcal{N} \) = 6 super Chern-Simons-matter theory. J. High Energ. Phys. 2010, 58 (2010). https://doi.org/10.1007/JHEP02(2010)058
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DOI: https://doi.org/10.1007/JHEP02(2010)058