Matter and singularities

TL;DR

This paper studies the geometric structure of matter representations from codimension two singularities in F-theory, constructing global models for 6D and 4D theories, revealing novel phase transitions and constraints on matter content.

Contribution

It provides a detailed local and global geometric analysis of matter representations in F-theory with SU(N) gauge groups, including new phase transitions and matter content constraints.

Findings

Identified new types of singularities and phase transitions in F-theory models.

Constructed global 6D and 4D F-theory models with specific matter representations.

Reproduced known 6D supergravity theories through geometric analysis.

Abstract

We analyze the structure of matter representations arising from codimension two singularities in F-theory, focusing on gauge groups SU(N). We give a detailed local description of the geometry associated with several types of singularities and the associated matter representations. We also construct global F-theory models for 6D and 4D theories containing these matter representations. The codimension two singularities encountered include examples where the apparent Kodaira singularity type does not need to be completely resolved to produce a smooth Calabi-Yau, examples with rank enhancement by more than one, and examples where the 7-brane configuration is singular. We identify novel phase transitions, in some of which the gauge group remains fixed but the singularity type and associated matter content change along a continuous family of theories. Global analysis of 6D theories on P^2 with 7-branes wrapped on curves of small degree reproduces the range of 6D supergravity theories identified through anomaly cancellation and other consistency conditions. Analogous 4D models are constructed through global F-theory compactifications on P^3, and have a similar pattern of SU(N) matter content. This leads to a constraint on the matter content of a limited class of 4D supergravity theories containing SU(N) as a local factor of the gauge group.