WordNet sense 1 (a particular environment or walk of life):

area, arena, domain, orbit, sphere

WordNet sense 2 (the space around a radiating body within which its electromagnetic oscillations can exert force on another similar body not in contact with it):

field of force, force field

WordNet sense 3 (extensive tract of level open land):

plain, champaign

WordNet sense 4 (a piece of land prepared for playing a game):

playing field, athletic field, playing area

WordNet sense 5 (a region in which active military operations are in progress):

theater, theatre, field of operations, theater of operations, theatre of operations

WordNet sense 6 (a region where a battle is being (or has been) fought):

battlefield, battleground, field of honor, field of battle

WordNet sense 7 (a branch of knowledge):

bailiwick, discipline, study, subject, subject, branch of knowledge, field of study, subject area, subject field

WordNet sense 8 (the area that is visible (as through an optical instrument)):

field of view

WordNet sense 9 (a place where planes take off and land):

airfield, flying field, landing field

WordNet sense 10 (a particular kind of commercial enterprise):

field of operation, line of business