6 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 $N$ be a positive integer, let $B$ be a 2-form ${\mathbb Z}_N$ background, and let $\mathcal{P}(B)=B\cup B-B\cup_1 dB$ denote its Pontryagin square. The $'t$ Hooft anomaly clas…

Let $(M,\boldsymbol{g})$ be a $D$-dimensional Lorentzian manifold with conformal boundary $\partial M_c$. Let $(J, M, G)$ be an abelian gauge theory with gauge group $G$ and field…

In $(3+1)$-dimensional spacetime, consider bosonic topological orders without emergent fermions. Wang–Levin conjecture. Such topological orders are described by Dijkgraaf–Witten th…

Let $G$ be the group appearing in the skein construction, let $Z$ denote the relevant central subgroup, and let $\pi_1$ denote the corresponding fundamental-group twist. For a clos…

Let $\Gamma$ be a finite subgroup of $SU(3)$ defining an orbifold singularity $\mathbb{C}^3/\Gamma$. The abelianization–2-group conjecture. The structure of candidate 2-group symme…