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Summing Planar Open String Loops on a Worldsheet Lattice with Dirichlet and Neumann Boundaries | | Charles B. Thorn
; | | Date: |
19 Jun 2009 | | 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. | | Source: | arXiv, 0906.3742 | | Services: | Forum | Review | PDF | Favorites | |
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