Mapping 6D N = 1 supergravities to F-theory

TL;DR

This paper develops a systematic framework to realize anomaly-free 6D supergravity theories within F-theory, providing a geometric dictionary and analyzing models for consistency and potential quantum inconsistencies.

Contribution

It introduces a block-based approach to map 6D supergravity models to F-theory, including explicit construction of the geometric dictionary for simple gauge groups.

Findings

Constructed F-theory divisor dictionary for simple gauge groups

Identified 6D models possibly inconsistent with F-theory

Provided a systematic framework for model building in 6D supergravity

Abstract

We develop a systematic framework for realizing general anomaly-free chiral 6D supergravity theories in F-theory. We focus on 6D (1, 0) models with one tensor multiplet whose gauge group is a product of simple factors (modulo a finite abelian group) with matter in arbitrary representations. Such theories can be decomposed into blocks associated with the simple factors in the gauge group; each block depends only on the group factor and the matter charged under it. All 6D chiral supergravity models can be constructed by gluing such blocks together in accordance with constraints from anomalies. Associating a geometric structure to each block gives a dictionary for translating a supergravity model into a set of topological data for an F-theory construction. We construct the dictionary of F-theory divisors explicitly for some simple gauge group factors and associated matter representations. Using these building blocks we analyze a variety of models. We identify some 6D supergravity models which do not map to integral F-theory divisors, possibly indicating quantum inconsistency of these 6D theories.