2015
DOI: 10.1007/jhep03(2015)065
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Towards a C-function in 4D quantum gravity

Abstract: We develop a generally applicable method for constructing functions, C , which have properties similar to Zamolodchikov's C-function, and are geometrically natural objects related to the theory space explored by non-perturbative functional renormalization group (RG) equations. Employing the Euclidean framework of the Effective Average Action (EAA), we propose a C -function which can be defined for arbitrary systems of gravitational, Yang-Mills, ghost, and bosonic matter fields, and in any number of spacetime d… Show more

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Cited by 30 publications
(18 citation statements)
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“…At the level of the formalism, there has also been progress on computing properties and expectation values of the fluctuation fields around a given background [29][30][31][32][33]. By now it is appreciated that this type of computations, known as bi-metric computations, may be essential for precision computations of the properties of NGFP such as its critical exponents, addressing global aspects of gravitational RG flow by, e.g., establishing a suitable c-theorem [34], or establishing background-independence of the formalism [35].…”
Section: Jhep08(2015)113mentioning
confidence: 99%
“…At the level of the formalism, there has also been progress on computing properties and expectation values of the fluctuation fields around a given background [29][30][31][32][33]. By now it is appreciated that this type of computations, known as bi-metric computations, may be essential for precision computations of the properties of NGFP such as its critical exponents, addressing global aspects of gravitational RG flow by, e.g., establishing a suitable c-theorem [34], or establishing background-independence of the formalism [35].…”
Section: Jhep08(2015)113mentioning
confidence: 99%
“…As a self-consistent truncation scheme appears to be available for quantum gravity, the apparent convergence of fixed-point results is a key goal. It is fair to say that the status of results is rather encouraging with regard to this question, see [91,118,119,124,125,132,175,[185][186][187][188][189][190][191][192][193][194][195][196][197][198][199][200]. This has given rise to the general expectation that the Reuter fixed point indeed exists in full theory space, and provides a universality class for quantum gravity.…”
Section: The Convergence Questionmentioning
confidence: 96%
“…To do so we employ a sort of mean field analysis where O g µν ≈ O g sc k,µν , with g sc k,µν being the so-called self-consistent metric [82]. In the UV regime one then has…”
Section: The Geodesic Ball and The Geodesic Spherementioning
confidence: 99%