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

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 $W_{1+\infty }$ $\otimes$ $W_{1+\infty }$ $\to$ $W_{1+\infty }$ 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.

13 pages

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Cited by in corpus (7)

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• World-Sheet Duality, Space-Time Foam, and the Quantum Fate of a Stringy Black Hole
• Spacetime Diffeomorphisms and Topological W-Infinity Symmetry in Two Dimensional Topological String Theory
• As time goes by
• The String Universe: High $T_c$ Superconductor or Quantum Hall Conductor?