6D supergravity without tensor multiplets

TL;DR

The paper analyzes six-dimensional ${\cal N}=1$ supergravity theories without tensor multiplets, concentrating on gauge groups that are products of SU($N$) factors and their matter content. By exploiting anomaly cancellation and a Green–Schwarz type mechanism, the authors derive finite sets of allowable blocks parameterized by integers $b_i$ and link these low-energy data to F-theory via the Kodaira constraint, which bounds $\sum_i N_i b_i$ on the $B=\mathbb{P}^2$ base. They systematically enumerate single and multi-block models, revealing a spectrum of exotic matter representations (including 3- and 4-index antisymmetrics and tri-fundamentals) that can occur in rigid, anomaly-saturated configurations, some of which have no known string realizations yet. The results suggest potential new codimension-2 singularity structures in F-theory and highlight intriguing directions for UV completions and broader string constructions, while noting that several models violate the traditional Kodaira bound and may indicate novel string-theoretic mechanisms beyond established F-theory realizations.

Abstract

We systematically investigate the finite set of possible gauge groups and matter content for N = 1 supergravity theories in six dimensions with no tensor multiplets, focusing on nonabelian gauge groups which are a product of SU(N) factors. We identify a number of models which obey all known low-energy consistency conditions, but which have no known string theory realization. Many of these models contain novel matter representations, suggesting possible new string theory constructions. Many of the most exotic matter structures arise in models which precisely saturate the gravitational anomaly bound on the number of hypermultiplets. Such models have a rigid symmetry structure, in the sense that there are no moduli which leave the full gauge group unbroken.