Is it an Optimus laptop?
It is (taken from Sony US site - Z series speciffication):
Dynamic Hybrid Graphics
NVIDIAŽ GeForceŽ GT 330M GPU (1GB VRAM) with IntelŽ Graphics Media Accelerator HD
IntelŽ HM57 Express Chipset
HDMI™ out and VGA out
Key word - Dynamic Hybrid Graphics
So as far as we know... you can't use nVidia graphics under Linux but it will suck the power from your battery.
Are you happy?
You can do 2 things:
1) wait patiently until Linux developers in it's free time develop some means of use nVidia chip and disable it's power outage while not used, because nVidia developers won't do a thing;
2) sell it.
If you chose 1) option then go there -> https://launchpad.net/~hybrid-graphics-linux
, Join the team, subscribe mailing list and provide support as asked (some debug information from laptop system registers)
PS: another nice site for you to read and support with debug info -> http://linux-hybrid-graphics.blogspot.com/