Consistent Boundary Conditions for Open Strings

TL;DR

This paper investigates boundary conditions for various open string theories and supergravity, revealing the necessity of an infinite set of boundary conditions for consistent path integral quantization and the fundamental role of orientifolds.

Contribution

It systematically analyzes boundary conditions derived from symmetry principles and action extremization, introducing a boundary superspace formalism and highlighting the importance of orientifolds in open string quantization.

Findings

Corrections to Neumann boundary conditions due to bulk tachyon fields

Path integral quantization requires an infinite tower of boundary conditions

Orientifolds are fundamental in the path integral formulation of open strings

Abstract

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 Neumann boundary conditions, the description in terms of orientifolds is not just natural, but is actually fundamental.