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arXiv · 0709.2539

Multi-dimensional Virasoro algebra and quantum gravity

T. A. Larsson
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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.

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T. A. Larsson. 2007-09-17. Multi-dimensional Virasoro algebra and quantum gravity. https://arxiv.org/abs/0709.2539

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