Whilst Aretecracy is one nation and one nation alone, a military budget is still a necessary evil.
However it will be stripped back to the bare essentials. It will become purely a defence budget. As more nations join the Aretecratic Union, the military budgets of each nation will be lowered as the military might will be shared between them all as if there were one unit.
Eventually when the vast majority of the world is under Aretecratic rule, the military will be scrapped and focus will instead be diverted to planetary protection (defence of the planet from asteroids and other celestial events – I don’t think we need to deal with alien invasion yet).
The Nuclear Deterrent will remain
Whilst I’m a huge proponent of ending nuclear weapon stockpiling, at the moment it isn’t practical, however upon joining Aretecracy each member state will need to commit to destroying all nuclear missiles which are not actively being used in their defence program and creation of new nuclear weapons will be illegal.
As more and more nuclear capable nations join the AU, the weapons needed for active defence will diminish, the hope will be that sooner or later the number of nuclear weapons in existence in the world will trend towards zero.