The Origin of Space-Time as $W$ Symmetry Breaking in String Theory

TL;DR

This paper explores how space-time singularities in string theory can be understood through $W$ symmetry breaking, linking gauge theory, topological models, and the emergence of massless states.

Contribution

It introduces a novel interpretation of space-time singularities as $W$ symmetry breaking phenomena within a topological gauge framework of string theory.

Findings

Space-time singularities correspond to $W$ symmetry breaking.

Massless discrete states emerge as leg poles in the S-matrix.

Restoration of double $W$-symmetry explains the triviality of the high-energy S-matrix.

Abstract

Physics in the neighbourhood of a space-time metric singularity is described by a world-sheet topological gauge field theory which can be represented as a twisted $N=2$ superconformal Wess-Zumino model with a $W_{1+\infty} \otimes W_{1+\infty} $ bosonic symmetry. The measurable $W$-hair associated with the singularity is associated with Wilson loop integrals around gauge defects. The breaking of $W_{1+\infty}$ $\otimes $ $W_{1+\infty}$ $\rightarrow $ $W_{1+\infty}$ is associated with expectation values for open Wilson lines that make the metric non-singular away from the singularity. This symmetry breaking is accompanied by massless discrete `tachyon' states that appear as leg poles in $S$-matrix elements. The triviality of the $S$-matrix in the high-energy limit of the $c=1$ string model, after renormalisation by the leg pole factors, is due to the restoration of double $W$-symmetry at the singularity.