Exotic matter on singular divisors in F-theory

Understand

We analyze exotic matter representations that arise on singular seven-brane configurations in F-theory.

• We develop a general framework for analyzing such representations, and work out explicit descriptions for models with matter in the 2-index and 3-index symmetric representations of SU($N$) and SU(2) respectively, associated with double and triple point singularities in the seven-brane locus.
• These matter representations are associated with Weierstrass models whose discriminants vanish to high order thanks to nontrivial cancellations possible only in the presence of a non-UFD algebraic structure.
• This structure can be described using the normalization of the ring of intrinsic local functions on a singular divisor.