  The conserved Kardar-Parisi-Zhang equation in the presence of long-range
nonlinear interactions is studied by the dynamic renormalization group method.
The long-range effect produces new fixed points with continuously varying
exponents and gives distinct phase transitions, depending on both the
long-range interaction strength and the substrate dimension $d$. The long-range
interaction makes the surface width less rough than that of the short-range
interaction. In particular, the surface becomes a smooth one with a negative
roughness exponent at the physical dimension d=2.
