5 problems

Modulated-symmetry conjecture. Gauging the $p$-form symmetry gives a modulated symmetry in the dual theory, characterized by dipole algebra involving $(d-1-p)$-form and $q$-form di…

Let a finite symmetry $G$ be realized in a symmetry-preserving gapped theory, and let its ’t Hooft anomaly be the corresponding anomaly invariant. Torsion conjecture. The ’t Hooft…

Let $p$-dimensional excitations have a $(d-p-1)$-form symmetry with finite fusion group $G$ in $d$ spatial dimensions. Let $X$ be a simplicial complex triangulating the $d$-sphere…

Let $\rho$ be a state with anomalous symmetry $K\times G$, where $G$ has an onsite symmetry action, and let an FDLC denote a finite-depth local circuit. Strengthened anomaly obstru…

Anomalous boundary correspondence conjecture. Any two arbitrary boundary phases with the same quantum anomaly can transform into each other by symmetry-allowed operations, possibly…