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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
Abstract:
In this short note we answer a long standing question about the asymptotic
safety scenario for quantum gravity. The term asymptotic safety refers to the
conjecture that (i) the quantum field theory of gravity admits a non-trivial
ultraviolet fixed point, and that (ii) this has only a finite number of
relevant perturbations, i.e. a finite number of UV-stable directions (or in
other words, a finite number of free parameters to be fixed experimentally).
Within the f(R) approximation of the functional renormalization group equation
of gravity, we show that assuming the first half of the conjecture to be true,
the remaining half follows from general arguments, that is, we show that
assuming the existence of a non-trivial fixed point, the fact that the number
of relevant directions is finite is a general consequence of the structure of
the equations.
