14 problems

Let $M$ be a manifold, let $\Omega(M,*)$ denote the based loop space, and let $C(M,*)$ be the groupoid of based loops and homotopies between them. Let $N(M,*)$ be the normal monoid…

Let $G=SU(2)$, and let $\operatorname{Inn}G=G\xrightarrow{\operatorname{id}}G$ be the inner automorphism 2-group. The associated 4d BF-BB theory is a special case of 2-Chern-Simons…

Let $\mathcal{G}=(H\xrightarrow{t}G,\triangleright)$ be a crossed module of connected Lie groups. An adjustment is an algebraic datum given by a map…

Let $H$ be a compact, simple and simply connected Lie group, and let $\mathcal{G}_{\mathit{bas}}$ be its basic gerbe. Write … for the extension of smooth group objects in…

Trivial LGBs are associated with pre-classical theories. There exists a $\lambda \in \Omega^1(M;\mathcal{g})$ such that $\widetilde{\nabla^{\mathrm{YM}}}^{\lambda}$ is flat.

Trivial LGB flattening conjecture. If $\mathcal{G}$ is trivial, then there exists a field redefinition that makes $\nabla^{\mathrm{YM}}$ flat.

A 3+1-dimensional bosonic topological phase is a bosonic topological phase whose point-like particles are bosonic. Dijkgraaf–Witten realization conjecture. All 3+1-dimensional boso…

A crossed module of connected Lie groups is a crossed module whose underlying Lie groups are connected; an adjustment is the algebraic datum required to define a non-flat connectio…

Let $G_1\bowtie G_2$ be the group associated with the Lie algebra case, and let $G_1\ltimes G_2^*$ be the skeletal 2-group associated with the skeletal Lie 2-algebra case. Suppose…

The proposed theory refers to the three-dimensional theory discussed in the paper, with the $bκ$-Poincaré 2-group as its relevant 2-group structure. Discretization conjecture. Such…

The 2-Poincaré Yetter model is a lattice model associated with the Poincaré 2-group, while the KBF model is a state sum model of quantum flat spacetime developed by Baratin and Fre…

Let $M$ be a manifold and let ${\cal D}$ range over all discretizations of $M$. Denote by $\boldsymbol{\operatorname{Conn}} /\!/ \boldsymbol{\operatorname{Gauge}}(M,\mathcal{G})$ t…

Let $M$ be a manifold, let ${\cal D}_1$ and ${\cal D}_2$ be two different discretizations of $M$, and let $\mathcal{G}$ be the relevant higher gauge group. Denote by…

The effective BPS regimes of M2-branes and M5-branes are described in closely related ways. Palmer's conjecture. The descriptions of the effective BPS regimes of M2- and M5-branes…