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.
Highlights
In F-theory various aspects of the physics of intersecting seven-branes are captured by higher-dimensional two-torus fibered geometries
How can a non-Abelian discrete symmetry ever arise? This appears puzzling, since we know from the analysis of the Type IIB supergravity actions that non-Abelian discrete symmetries do occur in reductions with nonclosed forms representing torsion cohomology [36, 38]
Our findings suggest that torsion cohomology can only be ‘straightforwardly’ included for orientifold-even forms, i.e. where there are chains associated to the forms with non-vanishing physical volume
Summary
We briefly review the realisation of discrete gauge symmetries in field theory [30, 36, 39]. We include a discussion of supersymmetry and comment on the structure of non-minimal gauge-kinetic terms for non-Abelian groups that are neither semisimple nor compact
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