Twistor representation of null two-surfaces

We present a twistor description for null two-surfaces (null strings) in four-dimensional Minkowski space–time. The Lagrangian density for a variational principle is taken as a surface-forming null bivector. The proposed formulation is reparametrization invariant and free of any algebraic and differential constraints. The spinor formalism of Cartan–Penrose allows us to derive a nonlinear evolution equation for the world-sheet coordinate x a (τ,σ). An example of null two-surface given by the two-dimensional self-intersection (caustic) of a null hypersurface is studied.