String Universality in Six Dimensions

TL;DR

This paper explores the constraints on six-dimensional supergravity theories imposed by anomaly cancellation, demonstrating that many such theories correspond to string theory models, and proposing a conjecture of string universality in 6D.

Contribution

It establishes the equivalence of anomaly cancellation with string compactification constraints and introduces a conjecture that all consistent 6D supergravity theories have string theory realizations.

Findings

All consistent 6D supergravity theories with Lagrangian descriptions may have string theory realizations.

Identified a new infinite family of models satisfying anomaly factorization.

Found some infinite families of models to be pathological, indicating constraints on model consistency.

Abstract

In six dimensions, cancellation of gauge, gravitational, and mixed anomalies strongly constrains the set of quantum field theories which can be coupled consistently to gravity. We show that for some classes of six-dimensional supersymmetric gauge theories coupled to gravity, the anomaly cancellation conditions are equivalent to tadpole cancellation and other constraints on the matter content of heterotic/type I compactifications on K3. In these cases, all consistent 6D supergravity theories have a realization in string theory. We find one example which may arise from a novel string compactification, and we identify a new infinite family of models satisfying anomaly factorization. We find, however, that this infinite family of models, as well as other infinite families of models previously identified by Schwarz are pathological. We suggest that it may be feasible to demonstrate that there is a string theoretic realization of all consistent six-dimensional supergravity theories which have Lagrangian descriptions with arbitrary gauge and matter content. We attempt to frame this hypothesis of string universality as a concrete conjecture.