25 problems

Let $(A_1,D_3)$ be the Argyres-Douglas theory, and let $\mathfrak{su}(2)_{-4/3}$ denote the affine Lie algebra at level $-4/3$. Chiral-algebra conjecture. The chiral algebra corres…

Affine Kac–Moody chiral-algebra conjecture. The corresponding chiral algebra is

Let $K$ be a finitely generated free ${\cal D}_X$-module, and let $SK$ denote the associated chiral algebra. Let $\mathrm{def}_{SK}$ be its deformation pro-$*$-Lie algebra, and let…

Let $X$ be a smooth curve and let $M$ be a chiral algebra on $X$. Its deformations are controlled by a differential graded pro-$*$-Lie algebra $\mathfrak g$. A coisson algebra is a…

Let $\mathbb A^n$ be affine $n$-space, and let $D_n^\circ$ denote the relevant cohomological differential operator algebra. Consider the homotopy category of translation-equivarian…

The theory under consideration is the B-model topological string theory, or BCOV theory, with target $SL(2,\mathbb{C})$, holographically related to the protected chiral algebra sub…

Let $4\mathcal{A}4$ be a two-dimensional chiral algebra, let $4\operatorname{Vac}_{\mathrm{TI}}(\mathcal{A})4$ denote its space of translation-invariant vacua, and let…

Consider the chiral algebras associated with the toric Calabi–Yau threefolds … which are dual to $(p,q)$-webs of fivebranes, and the chiral algebra associated with a single Y-junct…

Beem–Rastelli conjecture. The single-trace BRST cohomology is generated by the symmetrized traces $A^{(n)}$ and their global super-conformal partners $B^{(n)}$, $C^{(n)}$, and…

Let $P$ be the index set appearing in the source, let $\mathcal{M}(k,\mu,\nu)$ be the proposed higher-rank generalization of the module $M_{r,s}$, and let…

Let $\mathcal{B}_k$ be the algebra constructed in the cited work, and let $W^{(2)}_{k-1}$ denote the corresponding algebra. The $\mathcal{B}_k$–$W^{(2)}_{k-1}$ isomorphism conjectu…

Let $(A_{N-1},A_{N(k-1)-1})$ denote the corresponding Argyres–Douglas theories, and let $\mathcal{B}(k)_{A_{N-1}}$ be the logarithmic algebra introduced for these theories. Creutzi…

Argyres-Douglas chiral algebra conjecture. The chiral algebra of the $(A_1,A_{2N})$ theory is the Virasoro minimal model with $(p,q)=(2,2N+3)$, while that of the $(A_1,D_{2N+1})$ t…

Let $chi[\mathcal{T}_X]$ be the chiral algebra associated with the four-dimensional theory $cmathcal{T}_X$. Let $T$ be a stress tensor, let $J_{su(2)}^A$ and $J_{su(3)}^I$ be affin…

Coulomb fixed-point correspondence. The $U(1)_r$ fixed points on ${\mathcal M}_{\mathcal T}$ are in one-to-one correspondence with the highest-weight modules of $\chi_{\mathcal T}$…

SCFT/chiral-algebra correspondence. The appropriate chiral algebra for ${\mathcal M}_H$ is the chiral algebra supplied by the SCFT/chiral algebra correspondence.

Refined-character conjecture. The fugacity $T$ counts the number of $L$ and $J$ generators used to construct states in the $\widehat{\mathfrak{su}}(2)$ module.

Refined-character conjecture. For an ${\cal N}=2$ superconformal field theory ${\cal T}$ with associated chiral algebra ${\cal A}[{\cal T}]$ and vacuum module ${\cal V}_{\cal T}$,…

Let $(J^b[k],F)$ be an Argyres–Douglas matter theory engineered from one irregular singularity without mass parameters and one full regular singularity. Let $J_{-k_F}$ denote the a…

The $D_{2n+2}$ Landau–Ginzburg model is expected to flow to the corresponding minimal model. Its chiral algebra contains the generators of the chiral ring, and a primary in the coh…

Let $(A_{k-1},A_{N-1})$ be the generalized Argyres–Douglas theory with $\operatorname{gcd}(k,N)=1$, so it has no flavor symmetry, and let $W_k$ denote the corresponding $W$-algebra…

Cylinder chiral algebra conjecture. The chiral algebra associated to a cylinder of type $\mathfrak{su}(n)$ is finitely generated by an $\widehat{\mathfrak{su}(n)}_{-n}$ affine curr…

qDS reduction conjecture. The chiral algebra associated to the class $\mathcal{S}$ theory with a puncture of type $\Lambda$ is obtained by performing qDS reduction with respect to…

Genus-zero chiral algebra conjecture. The protected chiral algebra is a $\mathcal{W}$-algebra with singlet generators $W_i$, $i=1,\ldots,n$, of dimension $i+1$, together with addit…

The Tn chiral algebra conjecture. The protected chiral algebra of the $T_n$ SCFT for any $n\geqslant3$ is a $\mathcal{W}$-algebra with the following generators: three sets of…