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The development of the N = 4 supersymmetric approach to quantum cosmology based on the non-compact global O(d,d) symmetries of the effective action is given. The N = 4 supersymmetric action whose bosonic sector is invariant under O(d,d) is determined. A representation for supercharges is obtained and the form of the zero and one-fermion quantum states leading to the Wheeler-DeWitt equation is found.The development of the N = 4 supersymmetric approach to quantum cosmology based on the non-compact global O(d,d) symmetries of the effective action is given. The N = 4 supersymmetric action whose bosonic sector is invariant under O(d,d) is determined. A representation for supercharges is obtained and the form of the zero and one-fermion quantum states leading to the Wheeler-DeWitt equation is found., Comment: 19 pages

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.