Non-Abelian discrete gauge symmetries in F-theory

TL;DR

This paper explores how non-Abelian discrete gauge symmetries naturally emerge in four-dimensional F-theory compactifications from seven-brane configurations, revealing new insights into their geometric and duality properties.

Contribution

It demonstrates the origin of non-Abelian discrete symmetries in F-theory from seven-brane setups and analyzes their structure via M-theory duality, including the role of fluxes and torsion cohomology.

Findings

Non-Abelian discrete symmetries arise from seven-brane configurations in F-theory.

The gauge coupling depends on gauged scalars and transforms non-trivially.

M-theory duality reveals the non-Abelian nature in the correct duality frame.

Abstract

The presence of non-Abelian discrete gauge symmetries in four-dimensional F-theory compactifications is investigated. Such symmetries are shown to arise from seven-brane configurations in genuine F-theory settings without a weak string coupling description. Gauge fields on mutually non-local seven-branes are argued to gauge both R-R and NS-NS two-form bulk axions. The gauging is completed into a generalisation of the Heisenberg group with either additional seven-brane gauge fields or R-R bulk gauge fields. The former case relies on having seven-brane fluxes, while the latter case requires torsion cohomology and is analysed in detail through the M-theory dual. Remarkably, the M-theory reduction yields an Abelian theory that becomes non-Abelian when translated into the correct duality frame to perform the F-theory limit. The reduction shows that the gauge coupling function depends on the gauged scalars and transforms non-trivially as required for the groups encountered. This field dependence agrees with the expectations for the kinetic mixing of seven-branes and is unchanged if the gaugings are absent.