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Read","submitted_at":"2001-06-14T20:08:22Z","abstract_excerpt":"We study two-dimensional nonlinear sigma models in which the target spaces are the coset supermanifolds U(n+m|n)/[U(1)\\times U(n+m-1|n)] \\cong CP^{n+m-1|n} (projective superspaces) and OSp(2n+m|2n)/OSp(2n+m-1|2n) \\cong S^{2n+m-1|2n} (superspheres), n, m integers, -2\\leq m\\leq 2; these quantum field theories live in Hilbert spaces with indefinite inner products. These theories possess non-trivial conformally-invariant renormalization-group fixed points, or in some cases, lines of fixed points. Some of the conformal fixed-point theories can also be obtained within Landau-Ginzburg theories. 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