14 problems

The dyon quantum electrodynamics (dQED) model is an alternative formulation of quantum electrodynamics with magnetic monopoles, based on the Cabibbo–Ferrari and Salam approach. Its…

Holomorphic VOA unitarity conjecture. Every holomorphic VOA is unitary.

Completeness conjecture. The results presented in the source cover all unitary and modular cases among these RTCs.

Positive-dimension unitarity conjecture. If

Let $\mathcal C_\ell(n)$ be the coset defined in the source, with $\ell\in\mathbb Z_{\geq1}$. Strong-unitarity conjecture. The vertex algebra $\mathcal C_\ell(n)$ is strongly unita…

Let $V$ be a vertex operator algebra of CFT type, meaning that $V$ has the standard nonnegative conformal-weight grading with vacuum in weight zero. Suppose that $V$ admits an inva…

Let $\mathfrak g=psl(2|2)$, $spo(2|m)$ with $m\geq 3$, $D(2,1;a)$, $F(4)$, or $G(3)$. Let $\nu$ be a dominant integral weight for $\mathfrak g^\natural$, let $\ell_0\in\mathbb R$,…

Let $\mathfrak g$ be a basic simple Lie superalgebra admitting a minimal Dynkin datum, let $W^k_{\min}(\mathfrak g)$ be its universal minimal $W$-algebra, and let…

Let $F$ be a non-archimedean local field with residue field $k$, let $\mathcal C$ be a curve over the ring of integers of $F$, and let $E_{\operatorname{Bun},1/2}$ be the Eisenstei…

Let … The source observes that both vertex algebras are positive, meaning that every irreducible module other than the algebra itself has positive conformal dimension. Unitarity co…

Let $|\lambda\rangle=E_{j_{n(w)}}^-\cdots E_{j_1}^-|\Lambda_s\rangle$ be a state in a finite-dimensional irreducible representation, and let $n_k$ and $\Lambda_i^k$ denote the coef…

Let $\chi(S,L)$ be the AdS phase shift defined by expressing the impact-parameter amplitude, including the disconnected piece, as … where the real constant $\mathcal{N}$ is fixed b…

In a quantum system with classical dynamics exhibiting collapsing trajectories, let the system's Hamiltonian have no ground state. Collapse-and-ground-state conjecture. The simulta…

To any simple Lie algebra $\mathfrak{g}$ and $q\in\mathbb C$ with $q^2$ a primitive $\ell$th root of unity, let $\mathcal{C}(\mathfrak{g},q,\ell)$ be the Hermitian premodular categ…