String interactions on the random lattice

TL;DR

This paper explores string interactions on a random lattice, deriving gauge field behaviors and interactions from scalar fields, and drawing parallels with string field theory to provide a novel perspective on gauge fields.

Contribution

It constructs a framework where gauge fields emerge as bound states of scalar fields on a random lattice, connecting lattice models with string field theory interactions.

Findings

States exhibit 1/p^2 propagators after tuning mass to zero

Constructed diagrams resemble 3-string vertices in string field theory

Derived Yang-Mills and F^3 interactions from lattice states

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.