71 problems

Let $d\geq 3$ and let the theory be a unitary bosonic conformal field theory that is not a topological quantum field theory. Let $\mathcal{E}(\tau)$ denote its dimensionless modula…

Let $d\geq 3$ and let the theory be a unitary bosonic conformal field theory that is not a topological quantum field theory. Let $\mathcal{E}(\tau)$ denote its dimensionless modula…

Let $V$ be a vertex operator algebra satisfying the conditions in the earlier conjecture on products of twisted intertwining operators, and let $G$ be a finite group of automorphis…

Let … where $\mathcal{F}_{M;m,\ell,n}$ are the Fock-space components in the decomposition of the $U_{x,p}(\widehat{\mathfrak{sl}}_2)$-module, and let $a$ satisfy…

Let $a=\log q$ for $q\in(0,1)$, and let $\mathbb{P}(N)(q)$ denote the probability of the annular crossing event $N$ described above. Set … Here $\eta$ denotes Dedekind's eta functi…

Let “free” plektons denote the class of free plektonic quantum field theories in $2+1$ dimensions, and let chiral conformal quantum field theories be conformal theories on a one-di…

Let a conformal quantum field theory have an associated hyperfinite type $4\mathrm{II}_1$ intertwiner algebra encoding combinatorial and topological data, and let the energy-moment…

Let $4\mathcal{A}(\mathcal{O})4$ be the algebra of a massive theory associated with a double cone $4\mathcal{O}4$, and let $4\omega_{m=0}4$ denote the conformally invariant vacuum…

Fix $i\in\{1,2,3\}$. Let $\mathbf{s}\in\mathbb{Z}_{\geq 0}^3$, $s_i>0$, $\Delta_j\in\mathbb{C}$ for $j\neq i$, and let the depth satisfy $t_i\in\{0,\ldots,s_i-1\}$. For non-negativ…

Geometrization conjecture. If $k$ is a positive integer divisible by $4$, every group-like element of

Let $G=ADE$ and let $G'$ be a folding of $G$. Write $\mathrm{CFT}(A_1,G)$ and $\mathrm{CFT}(A_1,G')$ for the two-dimensional conformal field theories associated with these Dynkin d…

CFT scaling-limit conjecture. The scaling limits of two-dimensional statistical mechanics models undergoing a continuous phase transition are given by the correlation functions of…

Let $(\cF,\cD,U,\Omega)$ be a potentially non-unitary Wightman conformal field theory on $S^1$ with invariant nondegenerate Hermitian form. Let $\cQ(I)=\cP(I)”$ be the associated a…

Let ${\cal A}$ be the cooperad governing the OPE data, let $H$ be the state space regarded as an ${\cal A}$-algebra, and let $\mathfrak g$ be the $L_{\infty}$-algebra controlling f…

Consider the collapsing family of unitary conformal field theories described above, with $\lambda_{\min}$ the minimal eigenvalue of the non-negative operator $L_0+\overline{L}_0$. R…

Consider a family of unitary conformal field theories with fixed central charge $c$, parameterized by $\varepsilon\to 0$, and closed surfaces $\Sigma$ in the family described by lo…

Fix $c_0\geq 0$ and $E_{\min}>0$, and let ${\cal M}_{c\leq c_0}^{E_{\min}}$ be the moduli space of irreducible conformal field theories with central charge $c\leq c_0$ and … For a gi…

Let $H=\bigoplus_{p,q}H^{p,q}$ be the state space of a conformal field theory, with $H^{1,0}$ its subspace of states of conformal weights $(1,0)$, and let the group of symmetries m…

Let $V_L$ be the lattice vertex operator algebra associated with the 128-dimensional Barnes–Wall lattice, and let $E(7)$ act on $V_L$. A holomorphic conformal field theory has cent…

Dimension conjecture. The dimension of the two-point variety is

Let $n$ growth points and $m$ screening variables define the null-vector equations and Ward identities for multiple radial SLE, and let $u\in\mathbb{H}$ be the marked interior poin…

Cartan-subalgebra conjugacy conjecture. All Cartan subalgebras of the conformal vertex algebra $V\otimes V_L$ are conjugate.

Let $\mathcal C^{(c=2)}_\varsigma$ be the constructed space spanned by the relevant Specht-polynomial solutions, and let $\mathcal S^{(c=2)}_\varsigma$ be the full solution space o…

Liouville completeness conjecture. Liouville conformal blocks form a complete basis with respect to the inner product above. This is the second mathematical gap in the rigorous def…

Let $c\geq 25$ and consider the inner product on conformal blocks … where $Z_{bc}$ is the ghost partition function and $Z_{26-c}$ is the timelike Liouville correlation function wit…