Chern-Simons theory from M5-branes and calibrated M2-branes

• Published in: The journal of high energy physics Vol. 2019; no. 8; pp. 1 - 70
• Main Authors: Mezei, Márk, Pufu, Silviu S., Wang, Yifan
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2019; Springer Nature B.V; SpringerOpen
• Subjects: Brane Dynamics in Gauge Theories; Branes; Calibration; Chern-Simons Theories; Classical and Quantum Gravitation; Elementary Particles; Feynman diagrams; Field theory; Field theory (physics); High energy physics; M-Theory; Operators; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quantum theory; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Supersymmetric Gauge Theory; Supersymmetry; Yang-Mills theory; Brane Dynamics in Gauge Theories; Chern-Simons Theories; M-Theory; Supersymmetric Gauge Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP08(2019)165

A bstract We study a sector of the 5d maximally supersymmetric Yang-Mills theory on S 5 consisting of 1 / 8-BPS Wilson loop operators contained within a great S 3 inside S 5 . We conjecture that these observables are described by a 3d Chern Simons theory on S 3 , analytically continued to a pure imaginary Chern-Simons level. Therefore, the expectation values of these 5d Wilson loops compute knot invariants. We verify this conjecture in the weakly-coupled regime from explicit Feynman diagram computations. At strong coupling, these Wilson loop operators lift to 1 / 8-BPS surface operators in the 6d (2 , 0) theory on S 1 × S 5 . Using AdS/CFT, we show that these surface operators are dual to M2-branes subject to certain calibration conditions required in order to preserve supersymmetry. We compute the renormalized action of a large class of calibrated M2-branes and obtain a perfect match with the field theory prediction. Finally, we present a derivation of the 3d Chern-Simons theory from 5d super-Yang-Mills theory using supersymmetric localization, modulo a subtle issue that we discuss.