Antimagic fields cause summoned creatures to wink out, I know:
Summoned creatures of any type wink out if they enter an antimagic field. They reappear in the same spot once the field goes away. Time spent winked out counts normally against the duration of the conjuration that is maintaining the creature. If you cast antimagic field in an area occupied by a summoned creature that has spell resistance, you must make a caster level check (1d20 + caster level) against the creature’s spell resistance to make it wink out. (The effects of instantaneous conjurations are not affected by an antimagic field because the conjuration itself is no longer in effect, only its result.)
My question is, how does that affect bound creatures? It also says: Elementals, undead, and outsider are likewise unaffected unless summoned. These creatures’ spell-like or supernatural abilities may be temporarily nullified by the field. Dispel magic does not remove the field.
The reason I'm confused is because I'm not sure how the gray area with summoning/binding/gate spells work. Are they unaffected, disappear until the antimagic field passes same as summoned creatures with effectively an unlimited summon duration, or do they disappear and not come back?