Several companies (Marlin, Ruger, Beretta) have 9 mm, .40 S & W and .45 ACP carbines, so with the AR (or M & P 15) platform I don't see why one couldn't be made. It's not a factory gun, if that is what you are asking.
It could be an S & W lower receiver with an aftermarket upper in .40 S & W. It would have to have either a different magazine well or an adapter for the pistol-sized magazines.
The Ruger rifles in pistol calibers that take their pistol magazines have been around for several years and have sold well. I think if Glock were to make a carbine that takes their pistol magazines they would sell millions of them. I'll bet most Police Depts. that carry Glocks would buy them, and I certainly would.
Are you listening, Gaston?
My guess is that it is an M&P lower with another brand's upper on there.
I've had an Olympic Arms upper in 9mm since about 1993 and it shoots flawlessly. I haven't shot the Oly Arms in .40 or .45 but my guess would be that it is comparable to the 9mm version with excellent fit and finish and reliability. They also have polymer magazines available versus the older modified Sten and Uzi magazines. Oly Arms even makes some versions with a dedicated mag well that will use Glock magazines which is great if you also carry a Glock sidearm in the same caliber so you can share magazines between the two weapons.
Needless-to-say the pistol caliber ammo is cheaper than .223/5.56 and in a defensive situation you don't have to worry as much about over penetration.