6 problems

Class S elliptic-genus VOA-character conjecture. The $(0,2)$ elliptic genus for $\mathcal{T}[C_{g,n}]$ should be a linear combination of the module characters of the associated VOA…

Unbroken U(1) gauge-group conjecture. At a generic point of the moduli space of chiral multiplets, the $\mathrm{U}(1)^g$ gauge group is unbroken.

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…