Tilings, Dimers and Quiver Gauge Theories

Amihay Hanany MIT

Abstract: This talk will describe a recent discovery on the relation between periodic tilings of the two dimensional plane, dimer coverings on such tilings, and gauge theories which arise in string theory - known as "quiver gauge theories". This is an elegant relation which solves a long standing problem in string theory that has to do with the physics of D branes probing singular manifolds. Besides the technical achievement in having such a relation, this opens up interesting connections between various areas of mathematical physics: Combinatorial dimer problems are used to count certain multiplicities associated with Calabi-Yau manifolds; A new class of SuperConformal Field Theories in 4 dimensions can be solved exactly; and the Kaluza Klein spectrum of certain 5 manifolds can be computed using algebraic methods. I will describe how dimers helped in getting the solutions to these problems.