Constraints on 6D Supergravity Theories with Abelian Gauge Symmetry

TL;DR

This paper investigates constraints on six-dimensional supergravity theories with abelian gauge factors, establishing finiteness conditions and identifying infinite families of theories with specific charge structures.

Contribution

It demonstrates the finiteness of gauge group combinations in certain 6D supergravity theories and explores the existence of infinite charge families not ruled out by current quantum consistency conditions.

Findings

Finiteness of gauge group and matter representations for theories with fewer than nine tensor multiplets.

Identification of infinite families of theories with distinct U(1) charges.

Only a finite subset of these theories can be realized in string theory.

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.