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 before and after a quiver mutation at the center node of a star-shaped quiver are equivalent.

In particular, it is known that a $D_4$-type quiver goes back to itself after finite times quiver mutations. 

We prove that  Gromov-Witten theories of the varieties obtained by those finite quiver mutations are equivalent with non-trivial transformations on their k\ahler variables.  

Furthermore, Gromov-Witten theory and k\ahler variables of $D_4$ go back to the original ones after finite times quiver mutations. 

This is a joint work with Weiqiang He.