Gauge theories from D7-branes over vanishing 4-cycles

TL;DR

This paper explores the complex dynamics of chiral quiver gauge theories on D7-branes over vanishing 4-cycles, including their geometric transitions, dualities, and noncommutative instanton structures, with implications for F-theory.

Contribution

It introduces a detailed analysis of D7-brane gauge theories with O7-planes, revealing their rich IR behavior and fuzzy internal dimensions, advancing understanding of F-theory limits.

Findings

Identification of anomaly cancellation mechanisms with O7-planes and flavor D7-branes.

Analysis of geometric transitions and dualities in these theories.

Demonstration of fuzzy internal dimensions emerging from the Higgs branch.

Abstract

We study quiver gauge theories on D7-branes wrapped over vanishing holomorphic 4-cycles. We investigate how to incorporate O7-planes and/or flavor D7-branes, which are necessary to cancel anomalies. These theories are chiral, preserve four supercharges and exhibit very rich infrared dynamics. Geometric transitions and duality in the presence of O-planes are analyzed. We study the Higgs branch of these quiver theories, showing the emergence of fuzzy internal dimensions. This branch is related to noncommutative instantons on the divisor wrapped by the seven-branes. Our results have a natural application to the recently introduced F(uzz) limit of F-theory.