Multi-dimensional Virasoro algebra and quantum gravity
Abstract
I review the multi-dimensional generalizations of the Virasoro algebra, i.e. the non-central Lie algebra extensions of the algebra vect(N) of general vector fields in N dimensions, and its Fock representations. Being the Noether symmetry of background independent theories such as N-dimensional general relativity, this algebra is expected to be relevant to the quantization of gravity. To this end, more complicated modules which depend on dynamics in the form of Euler-Lagrange equations are described. These modules can apparently only be interpreted as quantum fields if spacetime has four dimensions and both bosons and fermions are present.
Keywords
Cite
@article{arxiv.0709.2539,
title = {Multi-dimensional Virasoro algebra and quantum gravity},
author = {T. A. Larsson},
journal= {arXiv preprint arXiv:0709.2539},
year = {2007}
}
Comments
In: Mathematical physics research at the leading edge, ed: Charles V. Benton, pp 91-111, 2004 Nova Science Publishers Inc. ISBN 1-59033-905-3