Anomaly Inflow, Accidental Symmetry, and Spontaneous Symmetry Breaking

TL;DR

This paper explores the emergence of accidental symmetries and spontaneous symmetry breaking in 4d CFTs derived from 6d SCFTs on M5-branes, using geometric and holographic methods to analyze anomalies and central charges.

Contribution

It reveals how geometric considerations in M-theory uncover accidental symmetries and symmetry breaking not visible in field theory compactifications, and connects these to anomaly inflow and holography.

Findings

Identification of accidental symmetry in 4d CFTs from M-theory

Detection of spontaneous symmetry breaking of a U(1) generator

Agreement of computed central charges with holographic predictions

Abstract

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.