Frozen generalized symmetries

M-theory frozen singularities are (locally) D- or E-type orbifold singularities with a background fractional C3-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 N=1 gauge theory directly “freezes” to a lower-rank gauge theory due to the C3 background. This relies on a Hanany-Witten effect of fractional M5 branes and the presence of a gauge anomaly of fractional Dp probes in the circle reduction. Additionally, we compute defect groups and 8D symmetry topological field theories 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 T4/Γ with frozen singularities. We also revisit IIA ADE singularities with a C1-monodromy along a 1-cycle in the boundary lens space and show that this freezes the gauge degrees of freedom via confinement. Published by the American Physical Society 2025