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

Abstract

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.

16 pages 6 figures

References in corpus (8)

• A Worldsheet Description of Planar Yang-Mills Theory
• A Worldsheet Description of Large N_c Quantum Field Theory
• BT Worldsheet for Supersymmetric Gauge Theories
• The Fishnet as Anti-ferromagnetic Phase of Worldsheet Ising Spins
• A Mean Field Approximation to the Worldsheet Model of Planar phi^3 Field Theory
• Subcritical String and Large N QCD
• Nonabelian D-branes, Open Strings, and Gauge Theory
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Cited by in corpus (8)

• Summing Planar Diagrams by an Integrable Bootstrap II
• Summing Planar Diagrams by an Integrable Bootstrap
• Closed String Self-energy on the Lightcone Worldsheet Lattice
• Digitizing the Neveu-Schwarz Model on the Lightcone Worldsheet
• Open String Self-energy on the Lightcone Worldsheet Lattice
• A Note on High-Energy Scattering of Open Superstrings
• On Type 0 Open String Amplitudes and the Tensionless Limit
• 6-Vertex Model on an Open String Worldsheet