A New Anomaly-Free Gauged Supergravity in Six Dimensions

TL;DR

The paper presents a new anomaly-free six-dimensional $\mathcal{N}=1$ gauged supergravity with gauge group $E_7\times G_2\times U(1)_R$ and hypermatter in a half-hypermultiplet $(\mathbf{56},\mathbf{14})$, expanding the landscape of consistent $D=6$ theories. It shows how monopole compactifications on $\mathbb{R}^4\times \mathbf{S}^2$ can yield 4D effective theories with broken supersymmetry, driven by a positive-definite scalar potential arising from $U(1)_R$ gauging and by the structure of the hyperscalar manifold $Sp(392,1)/\bigl(Sp(392)\times Sp(1)_R\bigr)$. A detailed anomaly analysis confirms local and global consistency via Green-Schwarz factorization with explicit coefficients, ensuring anomaly cancellation. However, most monopole embeddings lead to perturbative instabilities due to tachyonic modes, except for the minimal embedding of the monopole in $U(1)_R$ (with $n=1$), which yields a stable vacuum preserving half of the original supersymmetry; this highlights both the potential for controlled stability and the challenges in achieving realistic 4D spectra from such constructions.

Abstract

We present a new anomaly-free gauged N=1 supergravity model in six dimensions. The gauge group is E_7xG_2xU(1)_R, with all hyperinos transforming in the product representation {56,14). The theory admits monopole compactifications to R^4xS^2, leading to D=4 effective theories with broken supersymmetry and massless fermions.