A control field is an area bounded by three links, forming a spherical triangle. Control fields capture mind units for the faction with which they are aligned, and they form the basis of global and regional scoring.
A control field is created when you establish a link between two portals which are both already linked to a third portal. Control fields only work in triangles of three connected portals; looping an area with five portals, for example, won’t make a field. (You can, however, create two more links to break that pentagon into three triangles, each of which will be a field.)
In order to ensure that you get maximum AP from your fields, it’s important that you completely understand the linking rules and use them to your advantage. The video below by Jonathan Baker explains this in detail:
Creating a control field earns you 1,250 AP, and awards your faction an amount of mind units according to the estimated population found under that field. Note that the estimated population is not exact; fielding bodies of water can still net a fair number of MU. Mind units stack, so nesting control fields allows you to gain MU from the same population multiple times.
A control field also inhibits linking inside it (except when the origin portal is one of the anchors of that field). As creating links and control fields are the actions which grant the most AP, this dampens leveling significantly by agents from both factions within the field.
A control field is destroyed when any of its three anchor portals drops its links due to enemy attacks or decay. As a portal’s resonators lose energy, the control fields attached to it start to take on a “tattered” appearance, and the effect is more pronounced the closer you are to that portal. If you see this in a friendly control field, you may want to shore up that portal to keep the field up; conversely, if it is an enemy field, that’s the anchor that will probably be easiest to attack to take down the field.