This is RP based.

I'm a trooper and, as far as I'm aware, the Republic holds no jurisdiction on Nar Shaddaa, particularly the Promenade and Slippery Slopes. In this way, I couldn't go up to somebody and apprehend them for bearing arms.

I stopped a fight from happening and was asked:

"Are you from CarSec?"

Who on earth are CarSec? Is it like CorSec, but for Nar Shadda - a security force owned by the Hutts?

If not, who are the main authorities on Nar Shaddaa?

This is RP based.

I'm a trooper and, as far as I'm aware, the Republic holds no jurisdiction on Nar Shaddaa, particularly the Promenade and Slippery Slopes. In this way, I couldn't go up to somebody and apprehend them for bearing arms.

I stopped a fight from happening and was asked:

"Are you from CarSec?"

Who on earth are CarSec? Is it like CorSec, but for Nar Shadda - a security force owned by the Hutts?

If not, who are the main authorities on Nar Shaddaa?

Cartel Security I'm assuming.

It is owned by the Hutt authorities as it's their world.

I'm not sure if it has changed or become more neutral (the Hutts were forced to do stuff after Makeb) depending on the timeline you RP in.

You could RP as CarSec if you wanted to, but I'm assuming you trying to be a good Republic trooper. My advice, don't get involved. Its mostly just Sith ERPing or underworld people doing other naughty things.

What's a Republic trooper doing there anyways?