Duality and dynamics of supersymmetric field theories from D-branes on singularities

Abstract

We carry out various investigations regarding gauge theories on the worldvolume of D-branes probing toric singularities. We first study the connection that arises in Toric Duality between different dual gauge theory phases and the multiplicity of fields in the gauged linear sigma models associated with the probed geometries. We introduce a straightforward procedure for the determination of toric dual theories and partial resolutions based on the (p, q) web description of toric singularities. We study the non-conformal theories that arise in the presence of fractional branes. We introduce a systematic procedure to study the resulting cascading RG flows, including the effect of anomalous dimensions on beta functions. Supergravity solutions dual to logarithmic RG flows are constructed, validating the field theory analysis of the cascades. We systematically study the IR dynamics of cascading gauge theories. We show how the deformation in the dual geometries is encoded in a quantum modification of the moduli space. We construct an infinite family of superconformal quiver gauge theories which are AdS/CFT dual to Sasaki-Einstein horizons with explicit metrics. The gauge theory and geometric computations of R-charges and central charges are shown to agree. We introduce new Type IIB brane constructions denoted brane tilings which are dual to D3-branes probing arbitrary toric singularities. Brane tilings encode both the quiver and superpotential of the gauge theories on the D-brane probes. They give a connection with the statistical model of dimers.

(cont.) They provide the simplest known method for computing toric moduli spaces of gauge theories, which reduces to finding the determinant of the Kasteleyn matrix of a bipartite graph.