Defects tied to discrete symmetries via bordism groups Ω^ξ_2(BG) and homology H_2(BG;Z) are codimension-two branes that participate in networks with junctions, expanding the Cobordism Conjecture's predictions in string-derived supergravity.
Non-Abelian discrete gauge symmetries in F-theory
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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.
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hep-th 1years
2026 1verdicts
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A missing link: Brane networks and the Cobordism Conjecture
Defects tied to discrete symmetries via bordism groups Ω^ξ_2(BG) and homology H_2(BG;Z) are codimension-two branes that participate in networks with junctions, expanding the Cobordism Conjecture's predictions in string-derived supergravity.