Chiral simple current extensions on the worldsheet reproduce and generalize obstructions to gauging center one-form symmetries in 6d and 8d string compactifications while clarifying BPS particle requirements upon circle reduction.
TASI Lectures on Abelian and Discrete Symmetries in F-theory
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abstract
In F-theory compactifications, the abelian gauge sector is encoded in global structures of the internal geometry. These structures lie at the intersection of algebraic and arithmetic description of elliptic fibrations: While the Mordell--Weil lattice is related to the continuous abelian sector, the Tate--Shafarevich group is conjectured to encode discrete abelian symmetries in F-theory. In these notes we review both subjects with a focus on recent findings such as the global gauge group and gauge enhancements. We then highlight the application to F-theory model building.
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String probes, simple currents, and the no global symmetries conjecture
Chiral simple current extensions on the worldsheet reproduce and generalize obstructions to gauging center one-form symmetries in 6d and 8d string compactifications while clarifying BPS particle requirements upon circle reduction.