The Tantalus field was a secret device in the quarters of the Mirror Universe's Captain Kirk that let him observe anyone aboard and make them vanish instantly.
The Mirror Kirk had reached command through murder, and the Tantalus field allowed him to remove rivals without trace. It was hidden in his cabin and was known only to him and his companion, Marlena Moreau.
When the Prime Kirk found himself in the Mirror Universe in 2267, Marlena showed him the device. She later used it to eliminate Sulu's men when they threatened Kirk, and Kirk urged the Mirror Spock to use the field to bring about change in the Empire.