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Consistent boundary conditions for open strings. (English) Zbl 1027.83027
Summary: We study boundary conditions for the bosonic, spinning (NSR) and Green-Schwarz open string, as well as for (1+1)-dimensional supergravity. We consider boundary conditions that arise from (1) extremizing the action, (2) BRST, rigid or local supersymmetry, or $$\kappa$$(Siegel)-symmetry of the action, (3) closure of the set of boundary conditions under the symmetry transformations, and (4) the boundary limits of bulk Euler-Lagrange equations that are “conjugate” to other boundary conditions. We find corrections to Neumann boundary conditions in the presence of a bulk tachyon field. We discuss a boundary superspace formalism. We also find that path integral quantization of the open string requires an infinite tower of boundary conditions that can be interpreted as a smoothness condition on the doubled interval; we interpret this to mean that for a path-integral formulation of open strings with only Neuman boundary conditions, the description in terms of orientifolds is not just natural, but is actually fundamental.

##### MSC:
 83E30 String and superstring theories in gravitational theory 83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory 81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory 83E50 Supergravity 83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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