Seiberg Duality conjecture for star-shaped quivers and finiteness of Gromov-Witten thoery for D-type quivers

Abstract

This is the second work on Seiberg Duality. This work proves that the Seiberg duality conjecture holds for star-shaped quivers: the Gromov-Witten theories for two mutation-related varieties are equivalent. In particular, it is known that a $D$-type quiver goes back to itself after finite times quiver mutations, and we further prove that Gromov-Witten theory together with k\"ahler variables of a $D_3$-type quiver variety return to the original ones after finite times quiver mutations.