Discrete and higher-form symmetries in SCFTs from wrapped M5-branes

TL;DR

This work develops a gravity-side framework for determining 't Hooft anomalies of discrete and higher-form symmetries in 4d SCFTs engineered from wrapped M5-branes in M-theory. By analyzing 5d BF-type topological terms, their boundary conditions, and singleton boundary modes, the authors map bulk discrete gauge data to global discrete symmetries in the 4d theories and compute the inflow anomaly polynomial using differential cohomology. They apply the construction to M5-branes on a Riemann surface (BBBW) and to M5-branes at a $\mathbb{Z}_2$ singularity (GMSW), providing explicit expressions for the perturbative and discrete anomaly structures and highlighting how anomalies can be read off from bulk topological terms and boundary data. The results illuminate the role of boundary conditions, singleton modes, and higher-form symmetries in holography and offer a path toward exact anomaly computations including $O(1)$ corrections from wrapped branes.

Abstract

We analyze topological mass terms of BF type arising in supersymmetric M-theory compactifications to $AdS_5$. These describe spontaneously broken higher-form gauge symmetries in the bulk. Different choices of boundary conditions for the BF terms yield dual field theories with distinct global discrete symmetries. We discuss in detail these symmetries and their 't Hooft anomalies for 4d $\mathcal N = 1$ SCFTs arising from M5-branes wrapped on a Riemann surface without punctures, including theories from M5-branes at a $\mathbb Z_2$ orbifold singularity. The anomaly polynomial is computed via inflow and contains background fields for discrete global 0-, 1-, and 2-form symmetries and continuous 0-form symmetries, as well as axionic background fields. The latter are properly interpreted in the context of anomalies in the space of coupling constants.

Figures (2)

• Figure 1: Schematic depiction of the space $M_4$ comprised by the 2-sphere $S^2_\varphi$, the circle $S^1_\psi$, and the $\mu$ interval. The space $M_4$ is the blow-up resolution of $S^4/\mathbb Z_2$. The blow-up $\mathbb P^1$'s are identified with $S^2_\varphi$ at $\mu = \mu_\mathrm N$ and $\mu = \mu_\mathrm S$.
• Figure 2: Schematic depiction of the space $B_2$ described by the constrained coordinates \ref{['mu_coords']} with line element $d\mu_0^2 + d\mu_1^2 + d\mu_2^2$. We have also indicated the orientation of $\partial B_2$ used throughout this appendix.