Loop Variables and Gauge Invariant Interactions of Massive Modes in String Theory

TL;DR

This paper extends the loop variable approach to include interaction terms for massive string modes, revealing that the theory appears non-interacting in these variables and suggesting a truncation of full string equations.

Contribution

It generalizes the loop variable method to incorporate interactions, involving polynomial terms with lower mass modes, and proposes a new perspective on string interactions.

Findings

Interaction terms involve only lower mass modes

The equations are truncations of full string equations

In loop variables, the theory appears non-interacting

Abstract

The loop variable approach used earlier to obtain free equations of motion for the massive modes of the open string, is generalized to include interaction terms. These terms, which are polynomial, involve only modes of strictly lower mass. Considerations based on operator product expansions suggest that these equations are particular truncations of the full string equations. The method involves broadening the loop to a band of finite thickness that describes all the different interacting strings. Interestingly, in terms of these variables, the theory appears non-interacting.