The Wilson loop in the Gaussian Unitary Ensemble

2016/04/29 by Razvan Gurău, Gurau, Razvan
Mathematics · #60B20 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.1604.08856

openalex publication_date 2016/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the supersymmetric formalism we compute exactly at finite N the expectation of the Wilson loop in the Gaussian Unitary Ensemble and derive an exact formula for the spectral density at finite N. We obtain the same result by a second method relying on enumerative combinatorics and show that it leads to a novel proof of the Harer-Zagier series formula.

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