Anomaly Inflow, Accidental Symmetry, and Spontaneous Symmetry Breaking

We consider the 6d (1,0) SCFT on a stack of $N$ M5-branes probing a $\mathbb C^2/\mathbb Z_2$ singularity. In particular, we study its compactifications to four dimensions on a smooth genus-$g$ Riemann surface with non-trivial flavor flux, yielding a family of 4d CFTs. By tracking the M-theory origin of the global symmetries of the 4d CFTs, we detect the emergence of an accidental symmetry and the spontaneous symmetry breaking of a $U(1)$ generator. These effects are visible from geometric considerations and not apparent from the point of view of the compactification of the 6d field theory. These phenomena leave an imprint on the 't Hooft anomaly polynomial of the 4d CFTs, which is obtained from recently developed anomaly inflow methods in M-theory. In the large-$N$ limit, we identify the gravity dual of the 4d setups to be a class of smooth $AdS_5$ solutions first discussed by Gauntlett-Martelli-Sparks-Waldram. Using our anomaly polynomial, we compute the conformal central charge and a non-Abelian flavor central charge at large $N$, finding agreement with the holographic predictions.