THE ORIGIN OF SPACE-TIME AS W-SYMMETRY BREAKING IN STRING THEORY

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 super-conformal Wess-Zumino model with a W1+infinity x W1+infinity bosonic symmetry. The measurable W-hair associated with the singularity is associated with Wilson loop integrals around gauge defects. The breaking of W1+infinity x W1+infintity --> W1+infinity 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 renormalization by the leg pole factors, is due to the restoration of double W-symmetry at the singularity.