We investigate field theory puzzles occuring in the interplay between
supersymmetry and duality in the presense of rotational isometries (also known
as non-triholomorphic in hyper-Kahler geometry). We show that T-duality is
always compatible with supersymmetry, provided that non-local world-sheet
effects are properly taken into account. The underlying superconformal algebra
remains the same, and T-duality simply relates local with non-local
realizations of it. The non-local realizations have a natural description using
parafermion variables of the corresponding conformal field theory. We also
comment on the relevance of these ideas to a possible resolution of long
standing problems in the quantum theory of black holes.Comment: 16 pages, Latex; contribution to the proceedings of the 5th Hellenic
school and workshops on elementary particle physics, Corfu, 3-24 September
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