Toric Duality, Seiberg Duality and Picard-Lefschetz Transformations

TL;DR

This paper explores the relationship between toric duality, Seiberg duality, and Picard-Lefschetz transformations in quiver gauge theories, revealing a broader symmetry group that connects different gauge theories flowing to the same IR fixed point.

Contribution

It demonstrates that Picard-Lefschetz transformations extend Seiberg duality, introducing fractional duals that generate a larger symmetry group of gauge theories.

Findings

Toric duality can be understood as Seiberg duality in simple cases.

The set of all Seiberg dualities forms a group.

Picard-Lefschetz transformations generate a larger group including fractional Seiberg duals.

Abstract

Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a single node in the quiver forms a group which is contained in a larger group given by a set of Picard-Lefschetz transformations. This leads to elements in the group (sometimes called fractional Seiberg Duals) which are not Seiberg Duality on a single node, thus providing a new set of gauge theories which flow to the same universality class in the Infra Red.