String field actions from W-infinity

TL;DR

This paper derives string field actions from the $W_{}$ symmetry using the coadjoint orbit method, revealing scalar and generalized KdV type theories with tensor couplings.

Contribution

It introduces a novel approach to string field actions based on $W_{}$ symmetry and coadjoint orbits, connecting to scalar and tensor field theories.

Findings

Derivation of string actions from $W_{}$ symmetry.

Identification of scalar collective field theory on the simplest orbit.

Generalization to KdV type theories with tensor couplings.

Abstract

Starting from $W_{\infty}$ as a fundamental symmetry and using the coadjoint orbit method, we derive an action for one dimensional strings. It is shown that on the simplest nontrivial orbit this gives the single scalar collective field theory. On higher orbits one finds generalized KdV type field theories with increasing number of components. Here the tachyon is coupled to higher tensor fields.