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2015

The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle

Grimm, Thomas W., Kapfer, Andreas, Klevers, Denis

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The geometry of elliptic fibrations translates to the physics of gauge theories in F-theory.

We systematically develop the dictionary between arithmetic structures on elliptic curves as well as desingularized elliptic fibrations and symmetries of gauge theories on a circle.
We show that the Mordell-Weil group law matches integral large gauge transformations around the circle in Abelian gauge theories and explain the significance of Mordell-Weil torsion in this context.
We also use Higgs transitions and circle large gauge transformations to introduce a group law for genus-one fibrations with multi-sections.

The Arithmetic of Elliptic Fibrations in Gauge Theories on a Circle · Around

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