Asymptotic safety in the f(R) approximation
Nov, 201266 pages
Published in:
- JHEP 01 (2013) 108
e-Print:
- 1211.0955 [hep-th]
Report number:
- SHEP-12-26
View in:
Citations per year
Abstract: (Springer)
In the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R > 0. We confront these with the requirement that a fixed point solution be smooth and exist for all R ≥ 0. Singularities induced by cutoff choices force the earlier versions to have no such solutions. However, we show that the most recent version has a number of lines of fixed points, each supporting a continuous spectrum of eigen-perturbations. We uncover and analyse the first five such lines. Sensible fixed point behaviour may be achieved if one consistently incorporates geometry/topology change. As an exploratory example, we analyse the equations analytically continued to R < 0, however we now find only partial solutions. We show how these results are always consistent with, and to some extent can be predicted from, a straightforward analysis of the constraints inherent in the equations.Note:
- Latex, 66 pages, published version, typos corrected
- topology: transition
- fixed point
- asymptotic safety
- quantum gravity
- gravitation: f(R)
References(42)
Figures(24)
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