#### Antisymmetric Wilson loops in \( \mathcal{N}=4 \) SYM: from exact results to non-planar corrections

Journal of High Energy Physics
August 2018, 2018:149 | Cite as
Antisymmetric Wilson loops in \( \mathcal{N}=4 \) SYM: from exact results to non-planar corrections
AuthorsAuthors and affiliations
Anthonny F. Canazas GarayAlberto FaraggiWolfgang Mück
Open Access
Regular Article - Theoretical Physics
First Online: 23 August 2018
Received: 19 July 2018
Accepted: 17 August 2018
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Abstract
We consider the vacuum expectation values of 1/2-BPS circular Wilson loops in \( \mathcal{N}=4 \) super Yang-Mills theory in the totally antisymmetric representation of the gauge group U(N) or SU(N). Localization and matrix model techniques provide exact, but rather formal, expressions for these expectation values. In this paper we show how to extract the leading and sub-leading behavior in a 1/N expansion with fixed ’t Hooft coupling starting from these exact results. This is done by exploiting the relation between the generating function of antisymmetric Wilson loops and a finite-dimensional quantum system known as the truncated harmonic oscillator. Sum and integral representations for the 1/N terms are provided.
Keywords 1/N Expansion AdS-CFT Correspondence Matrix Models Wilson, ’t Hooft and Polyakov loops
ArXiv ePrint: 1807.04052
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© The Author(s) 2018
Authors and Affiliations
Anthonny F. Canazas Garay1Alberto Faraggi2View author's OrcID profileWolfgang Mück34Email authorView author's OrcID profile1.Instituto de FísicaPontificia Universidad Católica de ChileSantiagoChile2.Departamento de Ciencias Fisicas, Facultad de Ciencias ExactasUniversidad Andres BelloSantiagoChile3.Dipartimento di Fisica “Ettore Pancini”Università degli Studi di Napoli “Federico II”NapoliItaly4.Istituto Nazionale di Fisica Nucleare, Sezione di NapoliNapoliItaly