Each Capitol has a Force Dome over it that protects it from all enemy intrusion. The Force Dome can only be taken down by ensuring that current Capitol owners own less than two of the Sub-Capitols. Once that occurs, the Dome goes down and your attack can begin. (When the Dome goes down, all the Sub-Capitol to Capitol lattice links (on the overhead map) will begin strobing to alert you to that fact.)
If the Defenders recapture at least two Sub-Capitols than the Dome will come up immediatly, and any attackers caught inside are instantly destroyed, though any hack in progress on the capital will still remain in effect. So, attackers will need to defend the Sub-Capitols as well as attack the Capitol.
An enemy touching the force dome generator (at the top) will be instantly killed, though the force dome itself acts as a wall. If the empire with the force dome is stupid enough to place a Router that goes to the inside of the dome, enemies can enter and will not be killed. However, the generator cannot be destroyed and any damage to base objects will not take NTUs to repair.