We generalise the SU(2) spinor framework of twisted geometries developed by
Dupuis, Freidel, Livine, Speziale and Tambornino to the Lorentzian case, that
is the group SL(2,C). We show that the phase space for complex valued Ashtekar
variables on a spinnetwork graph can be decomposed in terms of twistorial
variables. To every link there are two twistors---one to each boundary
point---attached. The formalism provides a new derivation of the solution space
of the simplicity constraints of loop quantum gravity. Key properties of the
EPRL spinfoam model are perfectly recovered.Comment: 18 pages, to appear in: Class. Quantum Gra
