Special Issue "Bipartite Graphs, Gauge Theories and Mirror Symmetry"

A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 May 2017)

Special Issue Editor

Guest Editor
Prof. Dr. Yang-Hui He

1. Department of Mathematics, City, University of London, Northampton Square, London EC1V 0HB, UK
2. Merton College, University of Oxford, Oxford OX1 4JD, UK
3. Nan Kai University, Tian Jin 300071, China
Website1 | Website2 | E-Mail
Interests: mathematical physics; string theory; algebraic geometry; number theory

Special Issue Information

Dear Colleagues,

We are compiling a Special Issue for Symmetry on the topic of quiver gauge theories, bipartite graphs and mirror symmetry. There has been a host of activity over the last decade on this exciting development, which resides at the intersection between quantum field theory, quiver representation theory, algebraic geometry and number theory, and has emerged has an important subject in mathematical physics. There have been several international conferences and workshops devoted to this area, and an increasing number of theoretical physicists, as well as pure and applied mathematicians, have been making contributions.

The subject began with the study of D-branes probing toric Calabi-Yau varieties in the context of AdS/CFT Correspondence in string theory, wherein the world-volume gauge theory is encoded in a quiver with relations. The representation variety of this quiver is, by construction, the affine toric Calabi-Yau variety. Over the years it was then realized that this data is graph dual to a bipartite graph on a torus, dubbed a “brane-tiling”.

The bipartite graph has a wealth of mathematical and physical information. Interpreted as a dimer model, the perfect matchings enumerated by the Kasteleyn matrix capture the geometrical information of the local mirror to the Calabi-Yau variety. Interpreted as a configuration of Neveu-Schwarz and Dirichlet-branes, the world-volume supports the supersymmetric gauge theory. More recently, interpreted as a dessin d’enfant, the shape of the underlying torus rigidifies to specific elliptic curves with number theoretic properties.

The purpose of the current volume is to gather some of these developments.

Prof. Dr. Yang-Hui He
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1200 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.


  • Supersymmetric Gauge Theory
  • Affine Calabi-Yau Varieties
  • Mirror Symmetry
  • Quivers

Published Papers

There is no accepted submissions to this special issue at this moment.
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