Bipartita: Physics, Geometry & Number Theory
Yang-Hui He
TL;DR
This paper explores the interdisciplinary connections between bipartite graphs, physics, geometry, and number theory, highlighting their applications in theoretical physics and mathematical models.
Contribution
It provides a concise overview of how bipartite graphs on Riemann surfaces relate to various physical theories and mathematical structures.
Findings
Bipartite graphs are integral to modeling physical phenomena.
Connections between graph theory and string theory are emphasized.
The paper offers an accessible introduction to complex interdisciplinary topics.
Abstract
Bipartite graphs, especially drawn on Riemann surfaces, have of late assumed an active role in theoretical physics, ranging from MHV scattering amplitudes to brane tilings, from dimer models and topological strings to toric AdS/CFT, from matrix models to dessins d'enfants in gauge theory. Here, we take a brief and casual promenade in the realm of brane tilings, quiver SUSY gauge theories and dessins, serving as a rapid introduction to the reader.
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Taxonomy
TopicsBlack Holes and Theoretical Physics · Algebraic Geometry and Number Theory · Algebraic structures and combinatorial models