Spectral dimension flow on continuum random multigraph

Giasemidis, Georgios; Wheater, J.F.; Zohren, Stefan

doi:10.1063/1.4758993

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2012

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“…Studying the spectral dimension from various different angles may unravel universal features in the quantum structure of spacetime. On more phenomenological grounds one can build toy models of spacetime which encompass special features of the spectral dimension [42]. Among further developments a fractional differential calculus [43] was used in [44,45] to assemble spacetimes with the fractal features observed in quantum gravity.…”

Section: Introductionmentioning

confidence: 99%

R2phase diagram of quantum Einstein gravity and its spectral dimension

2012

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Within the gravitational asymptotic safety program, the RG flow of the R 2 truncation in three and four spacetime dimensions is analyzed in detail. In particular, we construct RG trajectories which emanate from the non-Gaussian UV fixed point and possess long classical regimes where the effective average action is well approximated by the classical Einstein-Hilbert action. As an application we study the spectral dimension of the effective QEG spacetimes resulting from these trajectories, establishing that the picture of a multi-fractal spacetime is robust under the extension of the truncated theory space. We demonstrate that regimes of constant spectral dimensions can either be attributed to universal features of RG fixed points or singular loci in the β functions.

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Section: Introductionmentioning

confidence: 99%