Infinite order quantum-gravitational correlations

Abstract

A new approximation scheme for nonperturbative renormalisation group equations for quantum gravity is introduced. Correlation functions of arbitrarily high order can be studied by resolving the full dependence of the renormalisation group equations on the fluctuation field (graviton). This is reminiscent of a local potential approximation in O(N)-symmetric field theories. As a first proof of principle, we derive the flow equation for the "graviton potential" induced by a conformal fluctuation and corrections induced by a gravitational wave fluctuation. Indications are found that quantum gravity might be in a non-metric phase in the deep ultraviolet. The present setup significantly improves the quality of previous fluctuation vertex studies by including infinitely many couplings, thereby testing the reliability of schemes to identify different couplings to close the equations, and represents an important step towards the resolution of the Nielsen identity. The setup further allows in principle to address the question of putative gravitational condensates.

Form factors in asymptotic safety: conceptual ideas and computational toolbox

“…Here we used the symmetry in the two φ-fields to exchange the indices 2 and 3. By comparing (64) to (46) and (48), we see that split symmetry entails a specific relation between the form factors appearing in the vertex expansion. The (φφ)-vertex receives contributions from the scalar kinetic term only, and anticipating this we deliberately chose the same name for the two functions.…”

Asymptotically safe f(R)-gravity coupled to matter II: Global solutions

“…However, in the latter case the value of g 1 will change sign, and thus the solution becomes unphysical. If one uses now the type-II regulator for the fermions there will be a critical value of N D where g 1 becomes positive, for the solution (16) this value is N D = 14.1 whereas for the solution (17) it is N D = 12.9. If these values are exceeded the minimum turns to a maximum (but stays at the same location) and the values of g 1 and g 2 change sign.…”

“…For the solution (17) one obtains an interest- Table 1: Quadratic solutions for the fixed function with different matter content derived from the pure gravity solution (16). Table 2: Quadratic solution for the fixed function with different matter content derived from the pure gravity solution (17).…”

“…Note that such solu-tions of NGFP functions but for different truncations of the flow equation have been obtained in refs. [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Hereby the characteristics of the solutions for these functions differ significantly depending on the technical aspects of the respective work.…”

Momentum dependence of quantum critical Dirac systems

“…Notwithstanding, the pseudo-spectral method using Chebyshev rational functions [130][131][132] has proved to be a versatile and robust tool to obtain a solution of arbitrary accuracy, at least in principle. As an example from the FRG context, it has been used successfully to obtain high-accuracy solutions of effective potentials for various model systems before 68,89,90,94,[133][134][135][136] . We will therefore expand the couplings and the anomalous dimension function as a series of Chebyshev rational functions R n (n = 0, 1, .…”