9 problems

Let a four-dimensional $\mathcal{N}=2$ superconformal field theory be given, and consider decoupling relations in its operator product expansion. A bifiltered affine scheme is an a…

Let $P$ denote the relevant OPE data, and let $P^\sigma$ be its contribution in the permutation sector labeled by $\sigma$, with $P^{(1)}$ the sector associated with the identity p…

Let $\mathcal{T}_n$ and $\mathcal{T}^{\dagger}_n$ be conjugate twist fields in the $\mathbb{Z}_n$ orbifold of the non-compact boson, and let…

Let $I$ be an index set, let $D_\iota\in[0,d/2)$ for every $\iota\in I$, and let…

Let $V_q$ denote the fields associated with the point-contact operators, and let $V_{q_1}\times V_{q_2}$ denote the fusion of their Virasoro representations. The field…

Physicists' conjecture. Any reasonable quantum field theory satisfies the operator product expansion in the strong sense expressed by the EFNNB, without the $\frac{d}{2}$ restricti…

Let $\phi$ be the BMS field and $N[\phi^2]$ its renormalized square, with scaling exponents $[\phi]$ and $[\phi^2]$. Let $c_{1,1;0}$ and $c_{1,1;2}$ be constants. The spin-spin OPE…

Let two two-dimensional conformal field theories have central charge $c$, spectrum, and three-point functions for their operators. Finite-dimensional determination conjecture. Ther…

In the operator product expansion framework, let the OPE coefficients be constructed perturbatively for an interacting quantum field theory. Hollands' convergence conjecture. The p…