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Crystal melting, BPS quivers and plethystics

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  • Published: 06 June 2022
  • volume 2022, Article number: 16 (2022)
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Crystal melting, BPS quivers and plethystics
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  • Jiakang Bao  ORCID: orcid.org/0000-0002-9583-16961,2,
  • Yang-Hui He  ORCID: orcid.org/0000-0002-0787-83802,1,3,4 &
  • Ali Zahabi5,2 

  • 162 Accesses

  • 3 Citations

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A preprint version of the article is available at arXiv.

Abstract

We study the refined and unrefined crystal/BPS partition functions of D6-D2-D0 brane bound states for all toric Calabi-Yau threefolds without compact 4-cycles and some non-toric examples. They can be written as products of (generalized) MacMahon functions. We check our expressions and use them as vacuum characters to study the gluings. We then consider the wall crossings and discuss possible crystal descriptions for different chambers. We also express the partition functions in terms of plethystic exponentials. For ℂ3 and tripled affine quivers, we find their connections to nilpotent Kac polynomials. Similarly, the partition functions of D4-D2-D0 brane bound states can be obtained by replacing the (generalized) MacMahon functions with the inverse of (generalized) Euler functions.

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Authors and Affiliations

  1. Department of Mathematics, City, University of London, London, EC1V 0HB, U.K.

    Jiakang Bao & Yang-Hui He

  2. London Institute for Mathematical Sciences, Royal Institution, London, W1S 4BS, U.K.

    Jiakang Bao, Yang-Hui He & Ali Zahabi

  3. Merton College, University of Oxford, Oxford, OX1 4JD, U.K.

    Yang-Hui He

  4. School of Physics, NanKai University, Tianjin, 300071, P.R. China

    Yang-Hui He

  5. Institut de Mathématiques de Bourgogne, Université Bourgogne Franche-Comté, Dijon, France

    Ali Zahabi

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  1. Jiakang Bao
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Bao, J., He, YH. & Zahabi, A. Crystal melting, BPS quivers and plethystics. J. High Energ. Phys. 2022, 16 (2022). https://doi.org/10.1007/JHEP06(2022)016

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  • Received: 16 March 2022

  • Accepted: 09 May 2022

  • Published: 06 June 2022

  • DOI: https://doi.org/10.1007/JHEP06(2022)016

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Keywords

  • Brane Dynamics in Gauge Theories
  • Differential and Algebraic Geometry
  • Gauge Symmetry

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