The Action of the (Free) $\mathcal{N} = (3,1)$ Theory in Six Spacetime Dimensions

Understand

The action of the free $\mathcal{N} = (3,1)$ theory in six spacetime dimensions is explicitly constructed.

• The variables of the variational principle are prepotentials adapted to the self-duality conditions on the fields.
• The $(3,1)$ supersymmetry variations are given and the invariance of the action is verified.
• The action is first-order in time derivatives.