Often in other games capital ships have some sort of main super-cannon which causes enormous damage. Sometimes it's a beam weapon, ball of energy, etc. I believe that HAC capital ships should have a main cannon.

you mean like the Doomsday weapon Titan Class capital ships have in EVE?

or the teradon balls of death?

The E-Word has encroached on our sacred territory... Now it isn't Windows only...
Although it does have more limited support for Mac and Linux :)

Look at it this way;

Heavy Attack Cruiser/Carriers are woefully out-dated (the design is 300 years old, and Itani too boot!).

Tridents are, presumably, a more recent design, but they're far too small to mount massive weaponry, and are more commonly used as secure bulk-transports or escort craft for HACs

Teradons, being a very recent TPG design, do, in fact, field the sort of heavy weaponry you're suggesting. However, they're only destroyers, and lack the heavy protection that the HAC possesses.

Constellations are comparable in size and protective ability to the HAC, and are even fairly adept at combat themselves, being so new. However, their primary role is inherently non-violent, and fielding a heavy weapon would not be cost-effective (and the UIT is capitalist). Military refits of the craft may, in fact, exist, but no such reports are yet confirmed, and such tales are hardly credible.

And there is already a capital-ship busting weapon available to the major political powers, and its far more effective than an über-laser, and much more compact: the Avalon Nuclear Torpedo. The weapon suffers from heavy treaty restrictions, largely banning its use, but this hardly deters rouge factions like Corvus or the Akaneese, and the major, legitimate governments keep large stockpiles of the warheads (just in case). Anti-matter and Graviton warheads are presumed to exist, but all information on the subject is highly classified--and hotly denied.