14 problems

The field content of the three-dimensional theory comprises a two-dimensional metric $g_{\alpha\beta}$ and a scalar field $\phi$; constant scalar fields yield maximally symmetric t…

Dimensional reduction of ${\rm D}=11$ supergravity on tori gives a sequence of hidden symmetry groups $\mathrm{E}_n$, with reductions to lower dimensions requiring dualization of h…

For $d>2$, let $G(\mathrm{spacelike})$, $G(\mathrm{timelike})$, and $G(\mathrm{null})$ denote the groups obtained respectively from spacelike, timelike, and null dimensional reduct…

Barrier-removal conjecture. The barrier can be removed, so that Theorem holds in the larger Region $\mathrm{III}^{\prime}$.

Twisted-reduction conjecture. The $\mathbb{Z}_{2n+3}$-twisted circle reduction of the $(A_1,A_{2n})$ Argyres–Douglas theory results in the 3d rank-zero theory ${\mathcal{T}}_n$.

Let $\tilde a=0,\ldots,3$ label four-dimensional Lorentzian gamma matrices, and decompose the six-dimensional spinor as $\boldsymbol{\epsilon}^1=\zeta\otimes\eta$, where $\zeta$ is…

A five-dimensional superconformal field theory (5d SCFT) is a quantum field theory with five-dimensional superconformal symmetry. An untwisted or twisted circle reduction of a six-…

Higgs-branch survival conjecture. The vector space of Higgs branch Schur operators is not affected by the KK reduction.

Let $M^4_{\tilde{R}}\times\mathcal I_R$ be the five-dimensional spacetime obtained by reducing the purported six-dimensional Abelian $\mathcal N=(2,0)$ theory on a circle, and let…

Let $d\in\{3,4,5\}$, and consider solutions to the elliptic $\Phi^4$ equation in $\mathbb{R}^d$. A codimension $2$ hyperplane is an affine subspace of $\mathbb{R}^d$ of dimension…

Let $D$ be the dimension of the random-field Ising model, and set $D'=D-2$. The dimensional reduction conjecture. The critical exponents in dimension $D$ coincide with the correspo…

Consider a region containing many particles, represented as singularities, and let the associated metric have determinant and Weyl curvature that decrease on average as the number…

At the linearised level, dimensional reduction on a circle from six to five dimensions yields the linearised form of conventional Einstein maximal supergravity in five dimensions.…

Dimensional reduction conjecture. There exists a constant $\lambda=\lambda_d<1$ such that for all $n\geq 1$ there exists $m\geq 1$ such that all but…