Enforcement of laws is necessary, of course. Our model under a global democracy will be essentially the same as in individual countries today: an armed force will ensure the rule of law.
Enforcement authorities will be elected, directly, at various defined levels of jurisdiction: global, as well as levels that might correspond to today’s continents (or otherwise defined regions), countries, states/provinces, counties, and municipalities.
Notable differences from today’s enforcement structures include, first, the addition of a global layer, with subordination of smaller jurisdictions to it.
Second, robust citizen participation in our liquid democracy will limit the scope of executive/enforcement power, compared to countries like the US today. In today’s representative democracies, legislators preoccupied with reelection strive to avoid taking stands, so the legislative process fails. Executive power has expanded to fill the void, with little accountability. But with liquid democracy, many more decisions can be made by the people. This limits the grey areas left to the discretion of enforcement officials. Those who fear “big government” should find this comforting.
The enforcement authority, like the other elected positions described above, is subject to recall and swift replacement by deputies at any time.