Self-completeness and spontaneous dimensional reduction
Department of Physics, Loyola Marymount University, Los Angeles, CA, USA
2369 Frankfurt Institute for Advanced Studies (FIAS) & Institut für Theoretische Physik, J. W. Goethe-Universität, Frankfurt am Main, Germany
* e-mail: Jonas.Mureika@lmu.edu
Accepted: 28 June 2013
Published online: 25 July 2013
A viable quantum theory of gravity is one of the biggest challenges physicists are facing. We discuss the confluence of two highly expected features which might be instrumental in the quest of a finite and renormalizable quantum gravity —spontaneous dimensional reduction and self-completeness. The former suggests the spacetime background at the Planck scale may be effectively two-dimensional, while the latter implies a condition of maximal compression of matter by the formation of an event horizon for Planckian scattering. We generalize such a result to an arbitrary number of dimensions, and show that gravity in higher than four dimensions remains self-complete, but in lower dimensions it does not. In such a way we established an “exclusive disjunction” or “exclusive or” (XOR) between the occurrence of self-completeness and dimensional reduction, with the goal of actually reducing the unknowns for the scenario of the physics at the Planck scale. Potential phenomenological implications of this result are considered by studying the case of a two-dimensional dilaton gravity model resulting from dimensional reduction of the Einstein gravity.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2013