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Exact results and Schur expansions in quiver Chern-Simons-matter theories

  • Regular Article - Theoretical Physics
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  • Published: 05 October 2020
  • volume 2020, Article number: 22 (2020)
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Exact results and Schur expansions in quiver Chern-Simons-matter theories
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  • Leonardo Santilli1 &
  • Miguel Tierz2,1 

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A preprint version of the article is available at arXiv.

Abstract

We study several quiver Chern-Simons-matter theories on the three-sphere, combining the matrix model formulation with a systematic use of Mordell’s integral, computing partition functions and checking dualities. We also consider Wilson loops in ABJ(M) theories, distinguishing between typical (long) and atypical (short) representations and focusing on the former. Using the Berele-Regev factorization of supersymmetric Schur polynomials, we express the expectation value of the Wilson loops in terms of sums of observables of two factorized copies of U(N ) pure Chern-Simons theory on the sphere. Then, we use the Cauchy identity to study the partition functions of a number of quiver Chern-Simons-matter models and the result is interpreted as a perturbative expansion in the parameters tj = −e2πmj , where mj are the masses. Through the paper, we incorporate different generalizations, such as deformations by real masses and/or Fayet-Iliopoulos parameters, the consideration of a Romans mass in the gravity dual, and adjoint matter.

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Authors and Affiliations

  1. Grupo de Física Matemática, Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C6, 1749-016, Lisboa, Portugal

    Leonardo Santilli & Miguel Tierz

  2. Departamento de Matemática, Faculdade de Ciências, ISCTE - Instituto Universitário de Lisboa, Avenida das Forças Armadas, 1649-026, Lisboa, Portugal

    Miguel Tierz

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  1. Leonardo Santilli
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  2. Miguel Tierz
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Correspondence to Miguel Tierz.

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ArXiv ePrint: 2008.00465

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Santilli, L., Tierz, M. Exact results and Schur expansions in quiver Chern-Simons-matter theories. J. High Energ. Phys. 2020, 22 (2020). https://doi.org/10.1007/JHEP10(2020)022

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  • Received: 06 August 2020

  • Accepted: 06 September 2020

  • Published: 05 October 2020

  • DOI: https://doi.org/10.1007/JHEP10(2020)022

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Keywords

  • Matrix Models
  • Field Theories in Lower Dimensions
  • Chern-Simons Theories
  • Supersymmetric Gauge Theory

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