# Generic matter representations in 6D supergravity theories

## TL;DR

This paper characterizes the 'generic' matter representations in 6D supergravity theories, linking them to anomaly cancellation, moduli space dimensions, and F-theory constructions, and discusses implications for the string theory landscape and the standard model.

## Contribution

It defines and analyzes the concept of generic matter representations in 6D supergravity, connecting them to anomaly conditions and F-theory, and clarifies the distinction between generic and exotic matter.

## Key findings

- Generic matter representations are well-defined for 6D supergravity with multiple gauge factors.
- Most generic matter representations match those in F-theory models.
- Exotic matter requires more exotic singularities and is less generic.

## Abstract

In six-dimensional supergravity, there is a natural sense in which matter lying in certain representations of the gauge group is "generic," in the sense that other "exotic" matter representations require more fine tuning. From considerations of the dimensionality of the moduli space and anomaly cancellation conditions, we find that the generic sets of matter representations are well-defined for 6D supergravity theories with gauge groups containing arbitrary numbers of nonabelian factors and $\operatorname{U}(1)$ factors. These generic matter representations also match with those that arise in the most generic F-theory constructions, both in 6D and in 4D, with non-generic matter representations requiring more exotic singularity types. The analysis of generic versus exotic matter illuminates long-standing puzzles regarding F-theory models with multiple $\operatorname{U}(1)$ factors and provides a useful framework for analyzing the 6D "swampland" of apparently consistent low-energy theories that cannot be realized through known string constructions. We note also that the matter content of the standard model is generic by the criteria used here only if the global structure is $\operatorname{SU}(3)_\text{c} \times \operatorname{SU}(2)_\text{L} \times \operatorname{U}(1)_Y / \mathbb{Z}_6$.