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Quiver gauge theories: beyond reflexivity
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  • Regular Article - Theoretical Physics
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  • Published: 26 June 2020

Quiver gauge theories: beyond reflexivity

  • Jiakang Bao  ORCID: orcid.org/0000-0002-9583-16961,
  • Grace Beaney Colverd2 &
  • Yang-Hui He  ORCID: orcid.org/0000-0002-0787-83801,2,3 

Journal of High Energy Physics volume 2020, Article number: 161 (2020) Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Reflexive polygons have been extensively studied in a variety of contexts in mathematics and physics. We generalize this programme by looking at the 45 different lattice polygons with two interior points up to SL(2,ℤ) equivalence. Each corresponds to some affine toric 3-fold as a cone over a Sasaki-Einstein 5-fold. We study the quiver gauge theories of D3-branes probing these cones, which coincide with the mesonic moduli space. The minimum of the volume function of the Sasaki-Einstein base manifold plays an important role in computing the R-charges. We analyze these minimized volumes with respect to the topological quantities of the compact surfaces constructed from the polygons. Unlike reflexive polytopes, one can have two fans from the two interior points, and hence give rise to two smooth varieties after complete resolutions, leading to an interesting pair of closely related geometries and gauge theories.

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Authors and Affiliations

  1. Department of Mathematics, City University of London, Northampton Square, London, EC1V 0HB, UK

    Jiakang Bao & Yang-Hui He

  2. Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU, UK

    Grace Beaney Colverd & Yang-Hui He

  3. School of Physics, NanKai University, 94 Weijin Road, Tianjin, 300071, P.R. China

    Yang-Hui He

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  1. Jiakang Bao
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Bao, J., Colverd, G.B. & He, YH. Quiver gauge theories: beyond reflexivity. J. High Energ. Phys. 2020, 161 (2020). https://doi.org/10.1007/JHEP06(2020)161

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  • Received: 23 April 2020

  • Accepted: 02 June 2020

  • Published: 26 June 2020

  • DOI: https://doi.org/10.1007/JHEP06(2020)161

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Keywords

  • Brane Dynamics in Gauge Theories
  • Differential and Algebraic Geometry
  • Duality in Gauge Field Theories
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