Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry

TL;DR

This work analyzes six-dimensional ${ m N}=(1,0)$ supergravity theories with abelian and nonabelian gauge factors, focusing on anomaly cancellation and factorization constraints to bound the low-energy spectrum. It develops the general anomaly polynomial framework, including the generalized Green–Schwarz mechanism and linear multiplets, and derives explicit bounds on the number of ${U(1)}$ factors for $T<9$, establishing finiteness of nonabelian gauge/matter structures while allowing infinite families of distinct ${U(1)}$ charge assignments. The authors show that for $T o 9$ these finiteness results fail and construct infinite families of non-anomalous theories with arbitrarily many ${U(1)}$ factors, including examples realizable in F-theory; they also present nontrivial infinite ${U(1)}$ charge solutions that cannot be trivially extended to extra ${U(1)}$ factors. The findings motivate further exploration of stronger consistency constraints (potential Kodaira-type conditions) for abelian sectors and their geometric realizations, while clarifying the landscape of 6D ${ m N}=(1,0)$ theories and their UV completions.

Abstract

We study six-dimensional N=(1,0) supergravity theories with abelian, as well as non-abelian, gauge group factors. We show that for theories with fewer than nine tensor multiplets, the number of possible combinations of gauge groups - including abelian factors - and non-abelian matter representations is finite. We also identify infinite families of theories with distinct U(1) charges that cannot be ruled out using known quantum consistency conditions, though only a finite subset of these can arise from known string constructions.