Exotic matter on singular divisors in F-theory

• Main Authors: Klevers, Denis (Author), Morrison, David R. (Author), Raghuram, Nikhil (Contributor), Taylor IV, Washington (Contributor)
• Other Authors: Massachusetts Institute of Technology. Center for Theoretical Physics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor)
• Format: Article
• Language: English
• Published: Springer International Publishing AG, 2018-04-09T15:39:00Z.
• Subjects: Article
• Online Access: Get fulltext

 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. We consider the connection between geometric constraints on singular curves and corresponding constraints on the low-energy spectrum of 6D theories, identifying some new examples of apparent "swampland" theories that cannot be realized in F-theory but have no apparent low-energy inconsistency. Keywords: F-Theory; Differential and Algebraic Geometry; Supergravity Models; Superstring Vacua