TY - JOUR
T1 - Chern-Simons theory from M5-branes and calibrated M2-branes
AU - Mezei, Márk
AU - Pufu, Silviu S.
AU - Wang, Yifan
N1 - Funding Information:
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Publisher Copyright:
© 2019, The Author(s).
PY - 2019/8/1
Y1 - 2019/8/1
N2 - We study a sector of the 5d maximally supersymmetric Yang-Mills theory on S5 consisting of 1/8-BPS Wilson loop operators contained within a great S3 inside S5. We conjecture that these observables are described by a 3d Chern Simons theory on S3, 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 S1 × S5. 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.
AB - We study a sector of the 5d maximally supersymmetric Yang-Mills theory on S5 consisting of 1/8-BPS Wilson loop operators contained within a great S3 inside S5. We conjecture that these observables are described by a 3d Chern Simons theory on S3, 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 S1 × S5. 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.
KW - Brane Dynamics in Gauge Theories
KW - Chern-Simons Theories
KW - M-Theory
KW - Supersymmetric Gauge Theory
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U2 - 10.1007/JHEP08(2019)165
DO - 10.1007/JHEP08(2019)165
M3 - Article
AN - SCOPUS:85071729762
VL - 2019
JO - Journal of High Energy Physics
JF - Journal of High Energy Physics
SN - 1126-6708
IS - 8
M1 - 165
ER -