36 problems

The $(A_1,D_{2n+1})$ Zhu-algebra conjecture. The Zhu algebra of $\mathfrak{su}(2)_{-\frac{4n}{2n+1}}$ is isomorphic to $R$:

The $(A_1,D_{2n+1})$ Macdonald-index conjecture. The Macdonald index is

Andrews et al.'s conjecture. The specialization of the Macdonald index at $z=1$ satisfies

Let $\mathbf X$ be the singularity $x_1^5+x_2^3+x_2x_3^3+x_3x_4^2=0$, and let $\mathcal{T}_{\mathbf X}^{\rm 4d}$ be its associated four-dimensional theory. Let the Hasse diagram ob…

Let $\mathbf X$ be the isolated singularity … Let $\mathcal{T}_{\mathbf X}^{\rm 4d}$ be the associated four-dimensional theory, with the Coulomb-branch spectrum and central charges…

Let $\mathfrak{g}\in\{\mathfrak{a}_0,\mathfrak{a}_1,\mathfrak{a}_2\}$, let $M_{\mathfrak{g}}(q)$ denote the quantum monodromy, and let $h^\vee$ be the dual Coxeter number. For inte…

Affine-scheme conjecture. This affine scheme captures the Macdonald and Schur indices of the $(A_1,D_{2n+1})$ theory. The construction is supported in the paper by explicit agreeme…

Let $R_V$ be Zhu's $C_2$-algebra and let the Jacobi algebra be the algebra conjectured to be identical with $R_V$ for the relevant Argyres–Douglas theories. Jacobi-algebra obstruct…

Let $(q;q)_m=\prod_{j=1}^{m}(1-q^j)$ and let $\binom{2m}{k}_q$ be the $q$-binomial coefficient. The $(A_1,D_3)$ Macdonald-index conjecture. The Macdonald index of the Argyres–Dougl…

The $(A_1,A_4)$ identity. The displayed identity holds for all $m$. It extends the numerical agreement between the arc-space Hilbert series and the Macdonald index beyond the check…

Let $(A_1,A_2)$ denote the Argyres-Douglas theory, and label its four inequivalent higher sheets by $gamma=1,2,3,4$. The Lee-Yang TQFT, Fibonacci TQFT, and their conjugates form th…

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 $D_p^b(\mathfrak{sl}_N)$ be the Argyres–Douglas theory with maximal regular puncture, and let $m=\gcd(p,b)$, $n=b/m$, and $p=m(n+k)$. The 3d-mirror type I equivalence conjectur…

Let $D_p^{N-1}(\mathfrak{sl}_N,[Y])$ be a type II Argyres–Douglas theory, with $[Y]=[N^{l_N},\ldots,1^{l_1}]$. The type II/type I equivalence conjecture. It is equivalent to a type…

Let $D_p^b(\mathfrak{sl}_N,[Y])$ be an Argyres–Douglas theory with partition $[Y]=[N^{l_N},\ldots,1^{l_1}]$. The general type I equivalence conjecture. It is equivalent to a type I…

Let $[Y]=[N^{l_N},\ldots,1^{l_1}]$ be a partition of $N$, let $m=\gcd(b,p)$, and define … Let $[\widetilde Y_+]$ and $[\widetilde Y_-]$ be the partitions formed from its positive e…

Let $D_p^b(\mathfrak{sl}_N,[1^N])$ be the UV Argyres–Douglas theory with maximal regular puncture, whose puncture contributes a flavour symmetry $\mathfrak{su}(N)$. Write…

Let $D_p^b(\mathfrak{sl}_N,[Y])$ be a type $A$ Argyres–Douglas theory, with irregular flavour symmetry containing $\mathfrak{su}(N-b)\subset\mathfrak g_F^{\text{irreg}}$, and write…

Let $\scD^{(1)}_{\ell}$ be the $\ell$-dimensional module singled out among the four modules in the shortening regime, with basis indexed by $0\leq j\leq \ell-1$. Let…

Virasoro character–Macdonald index conjecture. The $t$-refined characters of the vacuum and next-to-vacuum modules satisfy

Let $\mathfrak{g}$ be the Langlands-dual Lie algebra associated with the twisted construction, let $f$ be the relevant nilpotent element, and let $W^{k_{2d}}(\mathfrak{g},f)$ denot…

Let $n$, $k$, $n_1$, and $n_2$ be parameters satisfying … and set $T_1=\operatorname{diag}(I_{n_1\times n_1},0_{n\times n})$ and…

Let $\mathfrak{j}$ be a simply laced Lie algebra of type $A$, $D$, or $E$, with rank $l$ and dual Coxeter number $h^{vee}$. Let $B_{p+1}(\mathfrak{j})$ be the corresponding vertex…

Let $\mathfrak{g}$ be the Lie algebra associated with the regular or irregular singularity, let $f$ be the relevant nilpotent orbit, and let $\mathrm{VOA}$ denote the two-dimension…

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…