The chiral anomaly from M theory

We argue that the chiral anomaly of $\mathcal{N}=1\mathrm{}$ 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 ${U\left(1\right)\mathrm{}}_R$ 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.