Connection between the Loop Variable Formalism and the Old Covariant Formalsm for the Open Bosonic String

TL;DR

This paper demonstrates the equivalence between the gauge invariant loop variable formalism and the old covariant formalism for open bosonic strings, showing they describe the same physics at tree level through explicit level-by-level mapping.

Contribution

It explicitly maps the fields, constraints, and gauge transformations between the two formalisms for the first two massive levels, suggesting a general equivalence at all levels.

Findings

Fields and gauge transformations can be mapped between formalisms.

The formalisms produce identical tree-level S-matrix results.

The equivalence holds in the critical dimension.

Abstract

The gauge invariant loop variable formalism and old covariant formalism for bosonic open string theory are compared in this paper. It is expected that for the free theory, after gauge fixing, the loop variable fields can be mapped to those of the old covariant formalism in bosonic string theory, level by level. This is verified explicitly for the first two massive levels. It is shown that (in the critical dimension) the fields, constraints and gauge transformations can all be mapped from one to the other. Assuming this continues at all levels one can give general arguments that the tree S-matrix (integrated correlation functions for on-shell physical fields) is the same in both formalisms and therefore they describe the same physical theory (at tree level).