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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.