15 problems

Let $G$ be a simple Lie group, and let $\widehat{\mathfrak{g}}$ denote the corresponding auxiliary three-dimensional quiver shape. Consider the Coulomb branch of this three-dimensi…

Let $\mathrm{Q}$ be a quiver defining a three-dimensional $\mathcal{N}=4$ quiver gauge theory with unitary gauge group, and let $(\widehat{Q},\widehat{W})$ denote the triple quiver…

Circular-quiver elliptic-genus character conjecture. The elliptic genus is a module character of the chiral algebra of the four-dimensional $\mathcal{N}=2$ circular quiver theory.

Equal-rank order-independence conjecture. The partition function $Z$ does not depend on the order of the NS5-branes. In particular, the resulting partition functions are related to…

Consider a bifundamental hypermultiplet connecting a short node and a long node in a folded, non-simply-laced quiver, with $r$ denoting the relevant root-length ratio. Extra-Fermi-…

Let $\fg$ be a simply-laced semisimple Lie algebra, let $\mu=\lambda-\alpha$ with $\lambda$ a dominant coweight and $\alpha$ a sum of positive coroots, and let $\CA^\vv_\fra$ be th…

Three-legged commutator conjecture.

Fundamental-to-tensor conjecture. For all $N$ and $r$,

Tachikawa's conjecture. All possible relations reduce to

Consider an $\mathcal N=4$ quiver with total gauge group $G\cong U(1)^\alpha$ and a decoupled overall $U(1)$ factor. Let $J$ and $K$ be the index sets of thimble contributions, let…

Let $G$ be a quiver gauge group of rank $\text{rank}(G)=\alpha$, and let $\widetilde{F}_{\infty}$ and $\widetilde{F}_{0}$ be the real-part restrictions of the asymptotic moduli-spa…

Dual linear quiver conjecture. The electric part of SQCD has a large number of dual linear quivers related to the original theory by $s$-confinement and symmetry enhancement.

Single-intersection conjecture. For general $m$, the index receives a contribution only from the intersection

Consider quiver gauge theories equipped with stability conditions, whose parameter space is divided into chambers corresponding to distinct stability regimes. Stability-chamber con…

A periodic quiver has nodes with coordinates, and Seiberg dualities produce partition functions associated to those nodes. Cluster-algebra invariance conjecture. If two different s…