Karta are mysterious artifacts introduced by YIIK I.V, and the main mechanic of I.V's Dark Game battle system. They can be placed in the Back (B) Middle (M) and Front (F) of a party member or an enemy to protect their HP. This doesn't completely protect them as a lucky pierce attack can go straight through the Karta and hit the HP directly.
Each Karta has powers, including stat upgrades and a unique passive ability. Once the Karta is destroyed however, these benefits are lost. The Karta can also be sacrificed for a special ability. Once a battle is complete, the player will regain all of their Karta back.
New Karta can be obtained by opening Foils found in the Mind Dungeon. They can be leveled up in the Mind Dungeon using Blood Bags, which are dropped occassionally by enemies in combat.
Field Cards are Karta that provide passive environmental effects, such as the ability to surpass hazards/blockades, altering how characters behave, or representing special items. They don't seem to have any combat use.
Exploring the Mind Dungeon has a "wing" Karta which allows Alex to jump, and a "camera" Karta which allows changing the camera to whatever angle you like.