Communications in Mathematical Physics

, Volume 313, Issue 1, pp 71–129 | Cite as

Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops

  • Vasily PestunEmail author


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.


Gauge Theory Vector Bundle Matrix Model Wilson Loop Elliptic Operator 
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Authors and Affiliations

  1. 1.Physics DepartmentPrinceton UniversityPrincetonUSA

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