Journal of High Energy Physics

, 2015:135 | Cite as

Gauge theories and dessins d’enfants: beyond the torus

  • Sownak BoseEmail author
  • James Gundry
  • Yang-Hui He
Open Access
Regular Article - Theoretical Physics


Dessin denfants on elliptic curves are a powerful way of encoding doubly-periodic brane tilings, and thus, of four-dimensional supersymmetric gauge theories whose vacuum moduli space is toric, providing an interesting interplay between physics, geometry, combinatorics and number theory. We discuss and provide a partial classification of the situation in genera other than one by computing explicit Belyi pairs associated to the gauge theories. Important also is the role of the Igusa and Shioda invariants that generalise the elliptic j-invariant.


Brane Dynamics in Gauge Theories AdS-CFT Correspondence Differential and Algebraic Geometry 


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.


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.St. Catherine’s CollegeUniversity of OxfordOxfordU.K.
  2. 2.Institute for Computational Cosmology, Department of PhysicsDurham UniversityDurhamU.K.
  3. 3.Somerville CollegeUniversity of OxfordOxfordU.K.
  4. 4.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeU.K.
  5. 5.Department of MathematicsCity UniversityLondonU.K.
  6. 6.School of PhysicsNanKai UniversityTianjinP.R. China
  7. 7.Merton CollegeUniversity of OxfordOxfordU.K.

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