Wave Functionals, Gauge Invariant Equations for Massive Modes and the Born-Infeld Equation in the Loop Variable Approach to String Theory

TL;DR

This paper details the wave functional in the loop variable approach to string theory, deriving gauge invariant equations for massive modes, and demonstrating how it reproduces both perturbative and non-perturbative (Born-Infeld) equations.

Contribution

It introduces a detailed description of the wave functional, showing its role in deriving gauge invariant equations for massive string modes and connecting perturbative and non-perturbative regimes.

Findings

Explicit examples of the wave functional are provided.

Gauge invariant equations for massive modes interacting with electromagnetism are derived.

The wave functional can reproduce Born-Infeld equations, linking to the sigma model approach.

Abstract

In earlier papers on the loop variable approach to gauge invariant interactions in string theory, a ``wave functional'' with some specific properties was invoked. It had the purpose of converting the generalized momenta to space time fields. In this paper we describe this object in detail and give some explicit examples. We also work out the interacting equations of the massive mode of the bosonic string, interacting with electromagnetism, and discuss in detail the gauge invariance. This is naturally described in this approach as a massless spin two field interacting with a massless spin one field in a higher dimension. Dimensional reduction gives the massive system. We also show that in addition to describing fields perturbatively, as is required for reproducing the perturbative equations, the wave functional can be chosen to reproduce the Born-Infeld equations, which are non-perturbative in field strengths. This makes contact with the sigma model approach.