Charge Lattices and Consistency of 6D Supergravity

TL;DR

This paper explores the mathematical structure of charge lattices in 6D supergravity, revealing that consistency requires the charge lattice to be self-dual, which constrains possible theories beyond anomaly cancellation.

Contribution

It extends known consistency conditions by linking charge lattice self-duality to anomaly cancellation constraints in 6D supergravity.

Findings

Charge lattice must be self-dual.

Anomaly cancellation determines a sublattice.

Self-duality constrains consistent theories.

Abstract

We extend the known consistency conditions on the low-energy theory of six-dimensional N = 1 supergravity. We review some facts about the theory of two-form gauge fields and conclude that the charge lattice Gamma for such a theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions in the supergravity theory determine a sublattice of Gamma. The condition that this sublattice can be extended to a self-dual lattice Gamma leads to a strong constraint on theories that otherwise appear to be self-consistent.