Torsion and quantum gravity
We suggest that the absence of torsion in conventional gravity could in fact be dynamical. A gravitational Meissner effect might produce instanton-like vortices of nonzero torsion concentrated at four-dimensional points; such torsion vortices would be the gravitational analogs of magnetic flux vortices in a type II superconductor. Ordinary torsion-free spacetime would correspond to the field-free superconducting region of a superconductor; a dense phase of “torsion foam” with vanishing metric but well-defined affine connection might be the analog of a normal conductor.
KeywordsPrincipal Bundle Topological Invariant Instanton Solution Flat Connection Gravitational Instanton
Unable to display preview. Download preview PDF.
- 1.A. A. Belavin, A. M. Polyakov, A. S. Schwarzand Yu. S. Tyupkin, Phys. Lett. 59B (1975) 85Google Scholar
- 2.G. 't Hooft, Phys. Rev. Lett. 37 (1976) 8; Phys. Rev. D14 (1976) 3432.Google Scholar
- 3.R. Jackiw and C. Rebbi, Phys. Rev. Lett. 37 (1976) 172; C. Callan, R. Dashen and D. Gross, Phys. Lett. (1976) 334.Google Scholar
- 4.T. Eguchi and A. J. Hanson, Phys. Lett. 74B (1978) 249; T. Eguchi and A. J. Hanson, submitted to Ann. Phys. (N. Y.).Google Scholar
- 5.S. W. Hawking and C. N. Pope, “Symmetry Breaking by Instantons in Supergravity” (DAMTP preprint); A. J. Hanson and H. Römer, “Gravitational Instanton Contribution to Spin 3/2 Axial Anomaly” (CERN, TH 2564).Google Scholar
- 6.V. A. Belinskii, G. W. Gibbons, D. N. Page and C. N. Pope, Phys. Lett. 76B (1978) 433.Google Scholar
- 7.G. W. Gibbons and S. W. Hawking, in preparation (private communication from S. W. Hawking).Google Scholar
- 8.N. Hitchin, private communication.Google Scholar
- 9.S. S. Chern, Ann. Math. 46 (1945) 674; see also T. Eguchi, P. B. Gilkey and A. J. Hanson, Phys. Rev. D17 (1978) 423.Google Scholar
- 10.See S. W. Hawking, “Spacetime Foam” (DAMTP preprint) for a similar proposal in the more restrictive context of Einstein's theory of gravity.Google Scholar