Geometry of N=1 Dualities in Four Dimensions

TL;DR

This paper explores the geometric realization of N=1 dualities in four-dimensional theories through D-branes on Calabi-Yau threefolds, linking dualities to monodromy and 3-cycle relations, and connecting to BPS state decay phenomena.

Contribution

It provides a geometric framework for understanding N=1 dualities via Calabi-Yau threefolds and relates these to known phenomena like BPS state decay, offering new classical geometric derivations.

Findings

N=1 dualities correspond to monodromy relations among 3-cycles

Dualities for SU, SO, USp gauge groups are geometrically mapped

Connections established with BPS state decay in N=2 theories

Abstract

We discuss how N=1 dualities in four dimensions are geometrically realized by wrapping D-branes about 3-cycles of Calabi-Yau threefolds. In this setup the N=1 dualities for SU, SO and USp gauge groups with fundamental fields get mapped to statements about the monodromy and relations among 3-cycles of Calabi-Yau threefolds. The connection between the theory and its dual requires passing through configurations which are T-dual to the well-known phenomenon of decay of BPS states in N=2 field theories in four dimensions. We compare our approach to recent works based on configurations of D-branes in the presence of NS 5-branes and give simple classical geometric derivations of various exotic dynamics involving D-branes ending on NS-branes.