Sword of Damocles

is the symbol of the Kings. It's made of pure energy which manifests into a gigantic sword that hovers above the King's head whenever they use their powers.

Appearance
The swords of each King have a unique design. When the previous King dies and a new one is chosen, the new King materializes a sword that is different in design from the previous King's sword, as shown with Mikoto Suoh's sword and Anna Kushina's Red Sword of Damocles.

The Kings' swords are distinguished from each other by the Aura that pulsates around them. For example, Suoh's can be identified by the Red Aura, while Munakata's sword has Blue Aura pulsating around it.

Damocles Down
When the sword starts to crumble and decay, it's considered dangerous and is a sign that the owner is losing control of his/her power, and as such, the sword shows the truest image of its King's condition. When a King has reached its limit, Damocles Down occurs—the orb at the center of the sword will stop glowing or break into pieces, and the sword will come crashing down, thus killing the owner of the sword and everyone within a certain radius. However, this event could be prevented if the King is killed before the sword crashes into the the ground, in which case the sword will vaporize and vanish. 

Trivia

 * The sword which appears above the Kings is from an ancient Greek myth, where a man named Damocles was offered a chance to sit on a throne and rule by the king, but with a huge sword hanging above him by a thin thread. The hanging sword became known as The Sword of Damocles ever since.