Abstract
We use localization techniques to compute the expectation values of supersymmetric Wilson loops in Chern-Simons theories with matter. We find the path-integral reduces to a non-Gaussian matrix model. The Wilson loops we consider preserve a single complex supersymmetry, and exist in any \(\mathcal{N}= 2 \) theory, though the localization requires superconformal symmetry. We present explicit results for the cases of pure Chern-Simons theory with gauge group U(N), showing agreement with the known results, and ABJM, showing agreement with perturbative calculations. Our method applies to other theories, such as Gaiotto-Witten theories, BLG, and their variants.
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References
D. Gaiotto and E. Witten, Janus configurations, Chern-Simons couplings, and the theta-angle in N = 4 super Yang-Mills theory, arXiv:0804.2907 [SPIRES].
O. Aharony, O. Bergman, D.L. Jafferis and J. Maldacena, N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals, JHEP 10 (2008) 091 [arXiv:0806.1218] [SPIRES].
J. Bagger and N. Lambert, Gauge symmetry and supersymmetry of multiple M2-branes, Phys. Rev. D 77 (2008) 065008 [arXiv:0711.0955] [SPIRES].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, arXiv:0712.2824 [SPIRES].
J.H. Schwarz, Superconformal Chern-Simons theories, JHEP 11 (2004) 078 [hep-th/0411077] [SPIRES].
M. Mariño, Chern-Simons theory, matrix integrals and perturbative three-manifold invariants, Commun. Math. Phys. 253 (2004) 25 [hep-th/0207096] [SPIRES].
M. Aganagic, A. Klemm, M. Mariño and C. Vafa, Matrix model as a mirror of Chern-Simons theory, JHEP 02 (2004) 010 [hep-th/0211098] [SPIRES].
E. Witten, Quantum field theory and the Jones polynomial, Commun. Math. Phys. 121 (1989) 351.
S.-J. Rey, T. Suyama and S. Yamaguchi, Wilson loops in superconformal Chern-Simons theory and fundamental strings in anti-de Sitter supergravity dual, JHEP 03 (2009) 127 [arXiv:0809.3786] [SPIRES].
N. Drukker, J. Plefka and D. Young, Wilson loops in 3-dimensional N = 6 supersymmetric Chern-Simons theory and their string theory duals, JHEP 11 (2008) 019 [arXiv:0809.2787] [SPIRES].
B. Chen and J.-B. Wu, Supersymmetric Wilson loops in N = 6 super Chern-Simons-matter theory, Nucl. Phys. B 825 (2010) 38 [arXiv:0809.2863] [SPIRES].
M. Mariño, Les Houches lectures on matrix models and topological strings, hep-th/0410165 [SPIRES].
D. Gaiotto and X. Yin, Notes on superconformal Chern-Simons-matter theories, JHEP 08 (2007) 056 [arXiv:0704.3740] [SPIRES].
H. Lü, C.N. Pope and J. Rahmfeld, A construction of killing spinors on S n, J. Math. Phys. 40 (1999) 4518 [hep-th/9805151] [SPIRES].
Y. Fujii and K. Yamagishi, Killing spinors on spheres and hyperbolic manifolds, J. Math. Phys. 27 (1986) 979 [SPIRES].
O. Aharony, J. Marsano, S. Minwalla, K. Papadodimas and M. Van Raamsdonk, The Hagedorn/deconfinement phase transition in weakly coupled large-N gauge theories, Adv. Theor. Math. Phys. 8 (2004) 603 [hep-th/0310285] [SPIRES].
M. Benna, I. Klebanov, T. Klose and M. Smedback, Superconformal Chern-Simons theories and AdS 4/CFT 3 correspondence, JHEP 09 (2008) 072 [arXiv:0806.1519] [SPIRES].
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ArXiv ePrint: 0909.4559
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Kapustin, A., Willett, B. & Yaakov, I. Exact results for Wilson loops in superconformal Chern-Simons theories with matter. J. High Energ. Phys. 2010, 89 (2010). https://doi.org/10.1007/JHEP03(2010)089
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DOI: https://doi.org/10.1007/JHEP03(2010)089