Loop Variables and Gauge Invariant Exact Renormalization Group Equations for (Open) String Theory -II

TL;DR

This paper extends gauge invariant exact renormalization group equations to all higher string levels, constructing an interacting infinite tower of massive higher spins as a compactified massless theory, with explicit truncation and curved space generalization.

Contribution

It generalizes previous work to all higher string levels, providing a gauge invariant framework for an interacting tower of massive higher spins via compactification.

Findings

Constructed gauge invariant equations for all higher string levels.

Explicit truncation results at level 4 and 5.

Outlined generalization to curved spacetime.

Abstract

In arXiv:1202.4298 gauge invariant interacting equations were writ- ten down for the spin 2 and spin 3 massive modes using the exact renor- malization group of a world sheet theory. This is generalized to all the higher levels in this paper. An interacting theory of an infinite tower of massive higher spins is obtained. They appear as a compactification of a massless theory in one higher dimension. The compactification and consequent mass is essential for writing the interaction terms. Just as for spin 2 and spin 3, the interactions are in terms of gauge invariant field strengths and the gauge transformations are the same as for the free theory. This theory can then be truncated in a gauge invari- ant way by removing one oscillator of the extra dimension to match the field content of BRST string (field) theory. The truncation has to be done level by level and results are given explicitly for level 4. At least up to level 5, the truncation can be done in a way that preserves the higher dimensional structure. There is a relatively straightforward generalization of this construction to (arbitrary) curved space time and this is also outlined.