Particle/String field theory induced by W-gravity non-linear sigma models and the Grand String Symmetry

TL;DR

This paper explores the topological phase of string theory using a restricted $ abla_{w_}$ non-linear sigma model, connecting it with algebraic structures and second quantization, with implications for string compactification and background independence.

Contribution

It introduces a novel approach to string theory's topological phase via a $ abla_{w_}$ sigma model, linking it to homotopy algebras and second quantization.

Findings

Connection between $ abla_{w_}$ models and homotopy algebras

Construction of second quantized twistor space

Speculations on string compactification and background independence

Abstract

Preliminary investigations of the topological phase of string theory along the lines of a (restricted) $\dot{w}_{\infty}$ non-linear sigma model are provided. Gauge fixing the w gravity gauge fields by preserving a geometric identity Lorenz covariantizes the w-particle and gauge covariantizes the YM. The notion of foliation ghosts is introduced. Connection between $\dot{w}_{\infty}$ and homotopy associative algebras is indicated. The second quantized twistor space of string theory is constructed and compared with the first quantised one. Speculations about the relevance of the massive string fields to the compactification of the bosonic string down to four dimensions times the standard model group as well as to the solution of the background independence problem and the integration over moduli space problem are also provided.