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

John Ellis·N. E. Mavromatos·D. V. Nanopoulos
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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.

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John Ellis, N. E. Mavromatos, D. V. Nanopoulos. 1992-05-28. The Origin of Space-Time as $W$ Symmetry Breaking in String Theory. https://doi.org/10.1016/0370-2693(92)91949-a

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