The AC unit is causing positive pressure within the room. Positive pressure is when the pressure is greater than ambient. Since the pressure is higher in the room with AC, the air is constantly trying to equalize the pressure between the room and hallway. To do so it rushes out of the room through any crack or hole it can.
Cool Air sinks to the bottom of the floor. And since your AC exhaust usually isn’t placed on the floor the newly cooled air sinks on top of the already cool (but a bit warmer air since the floor is reheating the air). As such you get a high pressure zone as the coolest air is trying to sink down onto the ground. This squeezes the cool air which is already on the ground through the small gap below the door into the warmer hallway.
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