9 problems

Let $C$ be a punctured Riemann surface with refined pants decomposition $\widehat\sigma$, let $S$ be a set of $d$ degenerate insertions, and let $\varpi$ denote the associated disc…

Let ${\rm M5}$ and ${\rm WZ}$ denote the corresponding instanton and Wess–Zumino–Witten chiral partition functions, with twist elements ${\mathcal K}_e(\tau_e,x_e)$, Coulomb parame…

The W-algebra symmetry conjecture. The two-dimensional symmetry associated with the surface operator is $W(\widehat{\mathfrak{sl}}(N),\vec{N})$.

Let $SU(N)$ be a high-rank gauge group, and let the $A_{N-1}$ conformal Toda field theory be constrained by the $\W_N$ symmetry algebra. A degenerated vertex operator is an inserti…

Consider compactifications of the six-dimensional $(0,2)$ theory on a four-manifold $X_4$ with defects wrapping a punctured Riemann surface and filling a two-dimensional subspace o…

Let $G$ be an arbitrary gauge group, consider the pure four-dimensional theory with a surface operator of arbitrary type, and let the two-dimensional conformal field theory side ca…

In the NS limit, the Liouville background charge satisfies $Q\simeq b=\epsilon/\hbar$, and the degenerate Liouville operator relevant to the construction is … The corresponding ins…

Instanton counting for an $SU(N)$ superconformal gauge theory can be encoded by conformal blocks of $A_{N-1}$ Toda theory, with external momenta related to matter masses and intern…

Module-category conjecture. The 2-category of surface operators at $t=0$ can be described in terms of module categories over the monoidal category of boundary line operators for th…