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$$N=1$$ supersymmetric sigma model with boundaries. I. (English) Zbl 1028.81044
Summary: We study an $$N=1$$ two-dimensional nonlinear sigma model with boundaries representing, e.g., a gauge fixed open string. We describe the full set of boundary conditions compatible with $$N=1$$ superconformal symmetry. The problem is analyzed in two different ways: by studying requirements for invariance of the action, and by studying the conserved supercurrent. We present the target space interpretation of these results, and identify the appearance of partially integrable almost product structures.

MSC:
 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 81T10 Model quantum field theories 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 35Q58 Other completely integrable PDE (MSC2000)
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