Loop Variables and Gauge Invariant Interactions - II

TL;DR

This paper extends the loop variable approach to gauge invariant string interactions by implementing dimensional reduction, resulting in equations consistent with bosonic string spectra and scattering amplitudes, with off-shell gauge invariance.

Contribution

It introduces a dimensional reduction procedure for loop variable equations, aligning them with bosonic string spectra and demonstrating off-shell gauge invariance.

Findings

Equations reproduce bosonic string spectrum.

Scattering amplitudes match string theory results.

Off-shell gauge invariance is maintained.

Abstract

We continue the discussion of our previous paper on writing down gauge invariant interacting equations for a bosonic string using the loop variable approach. In the earlier paper the equations were written down in one higher dimension where the fields are massless. In this paper we describe a procedure for dimensional reduction that gives interacting equations for fields with the same spectrum as in bosonic string theory. We also argue that the on-shell scattering amplitudes implied by these equations for the physical modes are the same as for the bosonic string. We check this explicitly for some of the simpler equations. The gauge transformation of space-time fields induced by gauge transformations of the loop variables are discussed in some detail. The unintegrated (i.e. before the Koba-Nielsen integration), regularized version of the equations, are gauge invariant off-shell (i.e. off the {\em free} mass shell).