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

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