19 problems

Let ${\cal V}$ be the boundary vertex operator algebra of a three-dimensional theory, and let $R_{\cal V}$ denote its Zhu $C_2$ algebra. Write $\operatorname{Specm}(R_{\cal V})$ fo…

Quantum Hikita conjecture. For conical theories, the specialized quantum D-modules on Higgs branches and the D-modules of graded traces for Coulomb branches are isomorphic as D-mod…

Let $G$ be a reductive group, let $\mathbf{N}$ be a representation, and let $\mathcal{M}(G,\mathbf{N})$ and $\mathcal{M}_{\mathsf{Higgs}}(G,\mathbf{N})$ denote the associated Coulo…

Let $\mathcal{T}_{\mathbf X}^{\rm 4d}$ be the four-dimensional theory associated with the singularity $x_1^2+x_2x_4^4+x_2^3x_3+x_3^5x_4=0$. In the corresponding five-dimensional an…

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 $\mathrm{EQ}$ be a 3d $\mathcal{N}=4$ unitary quiver with good nodes only, and let its inversion procedure mean turning the relevant Hasse diagram upside down and replacing eac…

Let $\mathcal{T}$ be a four-dimensional $\mathcal{N}=2$ superconformal field theory with associated vertex operator algebra $V_{\mathcal{T}}$. Define Zhu's $C_2$-algebra by…

Let a three-dimensional abelian gauge theory be equipped with the A-twist and additional boundary free fermions, and let $V^A$ be the resulting boundary VOA. Write $X_{V^A}$ for it…

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…

Star-shaped quiver Coulomb-branch conjecture. The Coulomb branches of star-shaped quiver gauge theories are conjectured to be equivalent to the Higgs branches of 3D Sicilian theori…

Simple-pole conjecture. The construction relating the pole at $t_c$ to the low-energy theory extends to protected Higgs branch correlation functions, which also have a simple pole…

Let $\mathcal{V}$ be the boundary vertex algebra of an $A$-twisted gauge theory with purely free fermion boundary degrees of freedom. Its associated variety is … where…

The Higgs branch is a symplectic singularity with a Hasse diagram of symplectic leaves. For generalized toric polygons with mutually non-local 7-branes, the T-brane data are expect…

Assume that the Higgs-branch chiral ring is reduced. Let a two-dimensional vertex operator algebra (VOA) correspond to a four-dimensional $\mathcal{N}=2$ SCFT, and call it lisse wh…

Let a two-dimensional vertex operator algebra (VOA) correspond to a four-dimensional $\mathcal{N}=2$ SCFT, and let $\hat{\mathcal{B}}_R$ denote the class of Higgs-branch operators.…

A two-dimensional vertex operator algebra (VOA) corresponding to a four-dimensional $\mathcal{N}=2$ superconformal field theory (SCFT) has an associated variety, while the four-dim…

For a four-dimensional superconformal theory, let ${\cal I}_{HL}(t)$ denote the Hall–Littlewood limit of the superconformal index, and let…

Let ${\cal V}$ be the vertex operator algebra associated with a 4d Argyres-Douglas theory. Its Zhu $C_2$-algebra is … and its associated variety is…

The 4d ${\cal N}=2$ superconformal field theory/vertex operator algebra correspondence associates a meromorphic chiral algebra to a 4d theory, whose operators arise in the cohomolo…