The Toric SO(10) F-Theory Landscape

TL;DR

This paper classifies and analyzes six-dimensional F-theory models with SO(10) gauge symmetry using toric geometry, determining matter spectra, anomaly cancellation, and potential pathways to Standard Model-like theories.

Contribution

It provides a comprehensive geometric classification of SO(10) F-theory vacua, including matter spectra, anomaly computations, and connections to Standard Model phenomenology.

Findings

Complete matter spectra including singlets and charged states

Anomaly cancellation verified geometrically

Identification of models leading to Standard Model in four dimensions

Abstract

Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and analyze six-dimensional F-theory vacua with gauge group SO(10) taking into account Mordell-Weil U(1) and discrete gauge factors. We determine the full matter spectrum of these models, including charged and neutral SO(10) singlets. Based solely on the geometry, we compute all matter multiplicities and confirm the cancellation of gauge and gravitational anomalies independent of the base space. Particular emphasis is put on symmetry enhancements at the loci of matter fields and to the frequent appearance of superconformal points. They are linked to non-toric K\"ahler deformations which contribute to the counting of degrees of freedom. We compute the anomaly coefficients for these theories as well by using a base-independent blow-up procedure and superconformal matter transitions. Finally, we identify six-dimensional supergravity models which can yield the Standard Model with high-scale supersymmetry by further compactification to four dimensions in an Abelian flux background.