The mixed $0$-form/$1$-form anomaly in Hilbert space: pouring new wine into old bottles

Understand

We study four-dimensional gauge theories with arbitrary simple gauge group with $1$-form global center symmetry and $0$-form parity or discrete chiral symmetry.

• We canonically quantize on $\mathbb{T}^3$, in a fixed background field gauging the $1$-form symmetry.
• We show that the mixed $0$-form/$1$-form 't Hooft anomaly results in a central extension of the global-symmetry operator algebra.
• We determine this algebra in each case and show that the anomaly implies degeneracies in the spectrum of the Hamiltonian at any finite-size torus.