A Geometric Unification of Dualities

TL;DR

This paper explores the geometric origins of various dualities in N=1 quiver theories via type IIB D-brane probes on Calabi-Yau threefolds, unifying different dualities through geometric transitions and symmetries.

Contribution

It provides a geometric framework connecting Seiberg dualities, large N dualities, and duality cascades in N=1 quiver theories using Calabi-Yau transitions and Weyl group symmetries.

Findings

Geometric transitions correspond to Seiberg-like dualities and large N dualities.

Duality cascades are realized through affine Weyl group symmetries.

Unified geometric picture of dualities in N=1 quiver theories.

Abstract

We study the dynamics of a large class of N=1 quiver theories, geometrically realized by type IIB D-brane probes wrapping cycles of local Calabi-Yau threefolds. These include N=2 (affine) A-D-E quiver theories deformed by superpotential terms, as well as chiral N=1 quiver theories obtained in the presence of vanishing 4-cycles inside a Calabi-Yau. We consider the various possible geometric transitions of the 3-fold and show that they correspond to Seiberg-like dualities (represented by Weyl reflections in the A-D-E case or `mutations' of bundles in the case of vanishing 4-cycles) or large N dualities involving gaugino condensates (generalized conifold transitions). Also duality cascades are naturally realized in these classes of theories, and are related to the affine Weyl group symmetry in the A-D-E case.