Physical Society Colloquium

Interview for Faculty Position

Tilings, Dimers and Quiver Gauge Theories

Amihay Hanany

MIT

When D branes probe a singular CY manifold the gauge theory on the world volume of the brane gets dramatically changed. The details depend on the nature of the singularity and in all known cases lead to a quiver gauge theory. For toric singularities the gauge fields and matter fields are relatively easy to compute and there exist few equivalent methods for the computation. It has been a long standing problem to compute the superpotential which specifies how the matter fields couple to each other. In this lecture I will present a new concept - dimers - and will show how they simplify and solve the problem of computing the superpotential. Along the way we will find a new set of integers associated with a toric diagram, denoting the multiplicities of linear sigma model fields. The quiver gauge theories flow in the infrared to a superconformal fixed point, the details of it are captured using the AdS/CFT correspondence - A dual Sasaki-Einstein manifold arises for which some of its properties are exactly derived using the gauge theory description.

References (hep-th):
0504110 for a general introduction of dimers and their relation to quiver gauge theories, including many examples.
0503149 for the relation between dimers and multiplicities of toric diagrams.
0505211, 0505220 for tilings of L^abc manifolds.
0506232 for application to find R charges.
0508248 for the relation to a 2d Ising model on a triangular lattice.