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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 quantum actions of the (4,4) supersymmetric non-linear sigma model and its dual in the Abelian case are constructed by using the background superfield method. The propagators of the quantum superfield and its dual and the gauge fixing actions of the original and dual (4,4) supersymmetric sigma models are determined. On the other hand, the BRST transformations are used to obtain the quantum dual action of the (4,4) supersymmetric non-linear sigma model in the sense of Poisson-Lie T-duality, Comment: 18 pages

We construct the Generalized Monodromy matrix $\mathcal{\hat{M}}(\omega)$ of two dimensional string effective action by introducing the T-duality group properties.The integrability conditions with general solutions depending on spectral parameter are given. This construction is investigated for the exactly solvable Wess, Zumino, Novikov and Witten (WZNW) model in pp-wave Limit when B=0., Comment: 13 pages, No figures

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.