String interactions on the random lattice

Abstract

We combine two partons on a random lattice as a vector state. In the ladder approximation, we find that such states have 1/p^2 propagators (after tuning the mass to vanish). We also construct some diagrams which are very similar to 3-string vertices in string field theory for the first oscillator mode. Attaching 3 such lattice states to these vertices, we get Yang-Mills and F^3 interactions up to 3-point as from bosonic string (field) theory. This gives another view of a gauge field as a bound state in a theory whose only fundamental fields are scalars.