A systematic search for anomaly-free supergravities in six dimensions

TL;DR

This study conducts a systematic search for anomaly-free six-dimensional $\mathcal{N}=1$ supergravities with a single tensor multiplet by imposing a restricted set of gauge groups and hypermultiplet representations. It provides an exhaustive catalog of anomaly-free Poincaré theories and a constrained set of gauged theories, revealing many known models and several new ones, with gauged models yielding only a few highly structured examples (notably $E_7\times E_6\times U(1)_R$, $E_7\times G_2\times U(1)_R$, and $F_4\times Sp(9)\times U(1)_R$) and numerous additional abelian-coupled variants. The work clarifies the landscape of consistent $D=6$, $\mathcal{N}=1$ theories under the Green–Schwarz mechanism, connects several models to heterotic/F-theory constructions, and sets the stage for exploring broader factorization possibilities, more tensor multiplets, and nontrivial $U(1)$ charge assignments. Its results have potential implications for string/M-theory compactifications and the realization of four-dimensional phenomenology via monopole backgrounds, while also suggesting rich Higgsing hierarchies and dualities among six-dimensional theories.

Abstract

We conduct a systematic search for anomaly-free six-dimensional N=1 chiral supergravity theories. Under a certain set of restrictions on the allowed gauge groups and the representations of the hypermultiplets, we enumerate all possible Poincare and gauged supergravities with one tensor multiplet satisfying the 6D anomaly cancellation criteria.