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Journal of High Energy Physics

, 2019:96 | Cite as

Combinatorics of Wilson loops in \( \mathcal{N} \) 4 SYM theory

  • Wolfgang MückEmail author
Open Access
Regular Article - Theoretical Physics
  • 23 Downloads

Abstract

The theory of Wilson loops for gauge theories with unitary gauge groups is formulated in the language of symmetric functions. The main objects in this theory are two generating functions, which are related to each other by the involution that exchanges an irreducible representation with its conjugate. Both of them contain all information about the Wilson loops in arbitrary representations as well as the correlators of multiply­ wound Wilson loops. This general framework is combined with the results of the Gaussian matrix model, which calculates the expectation values of -BPS circular Wilson loops in N = 4 Super-Yang-Mills theory. General, explicit, formulas for the connected correlators of multiply-wound Wilson loops in terms of the traces of symmetrized matrix products are obtained, as well as their inverses. It is shown that the generating functions for Wilson loops in mutually conjugate representations are related by a duality relation whenever they can be calculated by a Hermitian matrix model.

Keywords

Matrix Models Wilson 't Hooft and Polyakov loops 1/N Expansion 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimento di Pisica “Ettore Pancini”Univermta degli Studi di Napoli “Federico II”NapoliItaly
  2. 2.Istituto Nazionale di Pimca NucleareSezione di NapoliNapoliItaly

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