Summing Planar Open String Loops on a Worldsheet Lattice with Dirichlet and Neumann Boundaries

Details Summing Planar Open String Loops on a Worldsheet Lattice with Dirichlet and Neumann Boundaries Summing Planar Open String Loops on a Worldsheet Lattice with Dirichlet and Neumann Boundaries

2009-06-19

arxiv.org/abs/0906.3742v1

Phys.Rev.D80:086010,2009

Physics

High Energy Physics

High Energy Physics - Theory

16 pages 6 figures

Scientific paper

10.1103/PhysRevD.80.086010

We extend the lightcone worldsheet lattice approach to string theory, proposed in 1977 by Giles and me, to allow for coincident D-branes. We find a convenient lattice representation of Dirichlet boundary conditions, which the open string coordinates transverse to the D-branes satisfy. We then represent the sum over all planar open string multi-loop diagrams by introducing an Ising spin system on the worldsheet lattice to keep track of the presence or absence of fluctuating boundaries. Finally we discuss a simple mean field treatment of the resulting coupled Ising/coordinate worldsheet system. The interplay between Neumann and Dirichlet boundary conditions leads to a richer phase structure, within this mean field approximation, than that found by Orland for the original system with only Neumann conditions.

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