Two-dimensional (4, 0) supergravity in harmonic superspace. The action and the matter couplings

The superfield formulation of the two-dimensional (4, 0) supergravity is developed using the harmonic superspace techniques. The different sets of constraints are given and their solutions are expressed in terms of an SU(2) self-dual torsion superfield and harmonic prepotentials. The pure auxiliary (4, 0) Einstein action generalizing the (2, 0) one is written down and the most general (4, 0) matter couplings are given.