Geometric dualities in 4d field theories and their 5d interpretation

TL;DR

This paper explores the geometric dualities in 4d N=1 gauge theories from D3-branes on toric singularities, introducing new methods to identify symmetries and interpret Seiberg duality via 5d theories and (p,q) webs.

Contribution

It develops a new approach using (p,q) webs to analyze dualities, flows, and symmetries in 4d theories, and offers a novel 5d interpretation of Seiberg duality.

Findings

New method for identifying global symmetries using brane webs

Interpretation of Seiberg duality as crossing curves of marginal stability in 5d

Analysis of dualities and flows between theories from geometric data

Abstract

We study four-dimensional N=1 gauge theories arising on D3-branes probing toric singularities. Toric dualities and flows between theories corresponding to different singularities are analyzed by encoding the geometric information into (p,q) webs. A new method for identifying global symmetries of the four-dimensional theories using the brane webs is developed. Five-dimensional theories are associated to the theories on the D3-branes by using (p,q) webs. This leads to a novel interpretation of Seiberg duality, as crossing curves of marginal stability in five dimensions.