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

Journal of High Energy Physics, Aug 2018

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.

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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 51 Downloads 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 Download to read the full article text 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. References [1] J.M. Maldacena, Wilson loops in large N field theories, Phys. Rev. Lett. 80 (1998) 4859 [hep-th/9803002] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar [2] S.-J. Rey and J.-T. Yee, Macroscopic strings as heavy quarks in large N gauge theory and anti-de Sitter supergravity, Eur. Phys. J. 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Anthonny F. Canazas Garay, Alberto Faraggi, Wolfgang Mück. Antisymmetric Wilson loops in \( \mathcal{N}=4 \) SYM: from exact results to non-planar corrections, Journal of High Energy Physics, 2018, 149, DOI: 10.1007/JHEP08(2018)149