Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.
On the number of relevant operators in asymptotically safe gravity
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abstract
The asymptotic safety scenario of gravity conjectures that (i) the quantum field theory of gravity exists thanks to the presence of a non-trivial ultraviolet fixed point of the renormalization group, and that (ii) the fixed point 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.
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Proper-time functional renormalization in $O(N)$ scalar models coupled to gravity
Proper-time FRG applied to gravity-coupled O(N) scalars largely reproduces scaling solutions and critical properties found with the effective average action, with some quantitative differences at finite and large N depending on improved schemes.