Mapping 6D N = 1 supergravities to F-theory

TL;DR

The paper develops a systematic framework to realize anomaly-free 6D (1,0) supergravities with one tensor multiplet in F-theory by decomposing gauge content into blocks and mapping each block to a divisor on a Hirzebruch base. It constructs an explicit block-to-F-theory dictionary, demonstrates this for SU(N) blocks with fundamental and antisymmetric matter, and extends to additional representations and groups, including explicit Weierstrass models on F_m for several cases. A central result is the finite enumeration of SU(N) block models (e.g., 16,418 for N>3) and the demonstration that many of these blocks admit topologically consistent F-theory realizations, while some blocks map to non-integral divisors, hinting at possible quantum inconsistencies or new string vacua. The work advances the program of connecting 6D anomaly constraints to concrete geometric realizations in F-theory, contributing to the broader goal of establishing string universality for chiral 6D supergravities and guiding future explorations of more general tensor and gauge structures.

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.