Bipartite Graphs, Gauge Theories and Mirror Symmetry
A special issue of Symmetry (ISSN 2073-8994).
Deadline for manuscript submissions: closed (31 May 2017) | Viewed by 627
Special Issue Editor
2. Merton College, University of Oxford, Oxford OX1 4JD, UK
Interests: AI-assisted mathematics; mathematical physics; string theory; algebraic geometry; number theory
Special Issues, Collections and Topics in MDPI journals
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
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Keywords
- Supersymmetric Gauge Theory
- Affine Calabi-Yau Varieties
- Mirror Symmetry
- Quivers
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