Ultraviolet Fixed Points in Conformal Gravity and General Quadratic Theories

Abstract

We study the beta functions for four-dimensional conformal gravity using two different parametrizations of metric fluctuation, linear split and exponential parametrization. We find that after imposing the traceless conditions, the beta functions are the same in four dimensions though the dependence on the dimensions are quite different. This indicates the universality of these results. We also examine the beta functions in general quadratic theory with the Einstein and cosmological terms for exponential parametrization, and find that it leads to results for beta functions of dimensionful couplings different from linear split, though the fact that there exists nontrivial fixed point remains the same and the fixed points also remain the same.

19 pages. v2: minor corrections, published version. arXiv admin note: text overlap with arXiv:1308.3398

References in corpus (9)

• Exact evolution equation for the effective potential
• Massive Gravity in Three Dimensions
• Asymptotic safety in higher-derivative gravity
• Fixed Points of Higher Derivative Gravity
• Taming perturbative divergences in asymptotically safe gravity
• Ghost-free, finite, fourth order D=3 (alas) gravity
• Search of scaling solutions in scalar-tensor gravity
• Renormalisation of Newton's constant
• Field Parametrization Dependence in Asymptotically Safe Quantum Gravity

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