Enhanced gauge symmetry in 6D F-theory models and tuned elliptic Calabi-Yau threefolds

Understand

We systematically analyze the local combinations of gauge groups and matter that can arise in 6D F-theory models over a fixed base.

• We compare the low-energy constraints of anomaly cancellation to explicit F-theory constructions using Weierstrass and Tate forms, and identify some new local structures in the "swampland' of 6D supergravity and SCFT models that appear consistent from low-energy considerations but do not have known F-theory realizations.
• In particular, we classify and carry out a local analysis of all enhancements of the irreducible gauge and matter contributions from "non-Higgsable clusters," and on isolated curves and pairs of intersecting rational curves of arbitrary self-intersection.
• Such enhancements correspond physically to unHiggsings, and mathematically to tunings of the Weierstrass model of an elliptic CY threefold.