The chiral anomaly from M theory
Umut Gursoy, Sean A. Hartnoll, Ruben Portugues
TL;DR
This work proposes that the chiral anomaly of ${\mathcal N}=1$ SYM has a dual description as spontaneous symmetry breaking in M-theory on $G_2$ holonomy manifolds, introducing the notion of a massive isometry carried by a nonisometric angle $\psi$ in the $G_2$ background. By analyzing fluctuations around this angle, the authors obtain a massive vector field whose mass arises from a Stückelberg-type mechanism, matching the expected chiral current behavior in the UV and remaining consistent with the full eleven-dimensional equations in key $G_2$ backgrounds. The study includes a detailed reduction to five dimensions and a comparison with known 5D predictions, as well as applications to the Maldacena-Núñez background and the Atiyah-Hitchin metric, illustrating both the potential and the limitations of this gravity-side dictionary. The results highlight the subtlety of UV chiral symmetry breaking in $G_2$ backgrounds, the role of supersymmetry in ensuring consistency, and open avenues for covariant formulations and quantum-corrected realizations of $U(1)\to\mathbb{Z}_{2N}$ within M-theory.
Abstract
We argue that the chiral anomaly of $\Ncal = 1$ super Yang-Mills theory admits a dual description as spontaneous symmetry breaking in M theory on $G_2$ holonomy manifolds. We identify an angle of the $G_2$ background dual to the anomalous $U(1)_R$ current in field theory. This angle is not an isometry of the metric and we therefore develop a theory of ``massive isometry'' to describe fluctuations about such angles. Another example of a massive isometry occurs in the Atiyah-Hitchin metric.