Frozen Generalized Symmetries

TL;DR

This paper investigates M-theory frozen singularities with $D$- or $E$-type orbifold backgrounds, revealing how fractional monodromies cause gauge theories to freeze to lower ranks and analyzing their global symmetries and defect structures.

Contribution

It provides a top-down derivation of gauge theory freezing due to $C_3$-backgrounds, computes defect groups and SymTFTs, and applies these results to string theory and supergravity contexts.

Findings

Gauge theories freeze to lower rank due to fractional monodromies.

Computed defect groups and symmetry topological field theories for frozen theories.

Clarified the role of $C_3$-monodromy in M-theory singularities and gauge symmetry confinement.

Abstract

M-theory frozen singularities are (locally) $D$- or $E$-type orbifold singularities with a background fractional $C_3$-monodromy surrounding them. In this paper, we revisit such backgrounds and address several puzzling features of their physics. We first give a top-down derivation of how the $D$- or $E$-type 7D $\mathcal{N}=1$ gauge theory directly ``freezes" to a lower rank gauge theory due to the $C_3$-background. This relies on a Hanany--Witten effect of fractional M5 branes and the presence of a gauge anomaly of fractional D$p$ probes in the circle reduction. Additionally, we compute defect groups and 8D symmetry topological field theories (SymTFTs) of the 7D frozen theories in several duality frames. We apply our results to understanding the evenness condition of strings ending on $O7^+$-planes, and calculating the global forms of supergravity gauge groups of M-theory compactified on $T^4/\Gamma$ with frozen singularities. In an Appendix, we also revisit IIA $ADE$ singularities with a $C_1$-monodromy along a 1-cycle in the boundary lens space and show that this freezes the gauge degrees-of-freedom via confinement.