Seiberg duality conjecture for Gromov–Witten invariants of quiver critical loci

Let $(\mathbf{Q},\mathbf{W},\mathbf{v})$ be a quiver with potential and dimension vector, with associated gauge group $\mathsf{G}$, representation space $\mathsf{N}$, stability condition $\theta$, quiver variety $X:=\mathsf{N}/\!/_{\theta}\mathsf{G}$, and superpotential $\mathsf{w}:X\to\mathbb C$. Let $Z:=\{d\mathsf{w}=0\}\subset X$ be the critical locus, and define $Z'$ similarly for the mutated quiver with potential $(\mathbf{Q}',\mathbf{W}',\mathbf{v}')$. Seiberg duality conjecture. The Gromov–Witten invariants, including the Gromov–Witten potential and $J$-function, of $Z$ and $Z'$ are equal up to a change of Kähler parameters. The transformation rule of the Kähler variables behaves like that of $\mathcal{X}$-cluster variables under quiver mutation. This conjecture expresses the expected enumerative relationship between theories related by Seiberg duality; the source provides no resolution status.