Seiberg Duality Conjecture for Star-Shaped Quivers and Finiteness of Gromov–Witten Theory for D-Type Quivers

Source abstract

Abstract This work proves that the Seiberg Duality Conjecture holds for star-shaped quivers: the Gromov–Witten theories of mutation-related varieties are equivalent. In particular, it is known that there are only finitely many quivers that are mutation equivalent to a $D$-type quiver. We prove that the Seiberg Duality Conjecture holds for all quivers that are mutation equivalent to a $D_{3}$-type quiver, and find the change of Kähler variables.