Localization of gauge theory on a four-sphere and supersymmetric Wilson loops. (English) Zbl 1257.81056
Summary: We prove conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators in the \({\mathcal N=4}\) supersymmetric Yang-Mills theory with a Gaussian matrix model. We also compute the partition function and give a new matrix model formula for the expectation value of a supersymmetric circular Wilson loop operator for the pure \({\mathcal N=2}\) and the \({\mathcal N=2^*}\) supersymmetric Yang-Mills theory on a four-sphere. A four-dimensional \({\mathcal N=2}\) superconformal gauge theory is treated similarly.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T25 | Quantum field theory on lattices |
| 81T80 | Simulation and numerical modelling (quantum field theory) (MSC2010) |
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
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