Ghost wavefunction renormalization in asymptotically safe quantum gravity

Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein–Hilbert truncation supplemented by the wavefunction renormalization of the ghost fields. The latter induces non-trivial corrections to the β-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point, in agreement with the asymptotic safety conjecture which also survives in the presence of extra dimensions. In four dimensions the ghost anomalous dimension at the fixed point is η*c = −1.8, supporting spacetime being effectively two dimensional at short distances.

[1]  M. Niedermaier,et al.  The Asymptotic Safety Scenario in Quantum Gravity , 2006, Living reviews in relativity.

[2]  Christian S. Fischer.  Infrared properties of QCD from Dyson-Schwinger equations , 2006 .

[3]  Daniel F Litim.  Fixed points of quantum gravity. , 2004, Physical review letters.

[4]  Frank Saueressig,et al.  Taming perturbative divergences in asymptotically safe gravity , 2009, 0902.4630.

[5]  M. Reuter,et al.  Quantum gravity at astrophysical distances , 2004 .

[6]  F. Saueressig,et al.  A Class of nonlocal truncations in quantum Einstein gravity and its renormalization group behavior , 2002 .

[7]  Frank Saueressig,et al.  Functional Renormalization Group Equations, Asymptotic Safety, and Quantum Einstein Gravity , 2007, 0708.1317.

[8]  F. Saueressig,et al.  Four‐derivative Interactions in Asymptotically Safe Gravity , 2009, 0909.3265.

[9]  J. Jurkiewicz,et al.  The spectral dimension of the universe is scale dependent. , 2005, Physical review letters.

[10]  Frank Saueressig,et al.  ASYMPTOTIC SAFETY IN HIGHER-DERIVATIVE GRAVITY , 2009, 0901.2984.

[11]  M. Reuter,et al.  Ultraviolet fixed point and generalized flow equation of quantum gravity , 2001 .

[12]  F. Saueressig,et al.  Renormalization group flow of quantum gravity in the Einstein-Hilbert truncation , 2002 .

[13]  Martin Reuter,et al.  Bare action and regularized functional integral of asymptotically safe quantum gravity , 2008, 0811.3888.

[14]  H. Gies,et al.  Asymptotically free scalar curvature-ghost coupling in quantum Einstein gravity , 2009, 0907.1828.

[15]  Martin Reuter,et al.  Bimetric Truncations for Quantum Einstein Gravity and Asymptotic Safety , 2009, 0907.2617.

[16]  Daniele Oriti.  Approaches to Quantum Gravity , 2009 .

[17]  A. Benini,et al.  Improved Schwinger-DeWitt techniques for higher-derivative perturbations of operator determinants , 2007, 0704.2840.

[18]  S. Weinberg.  Effective Field Theory, Past and Future , 2009, 0908.1964.

[19]  D. Litim.  Fixed points of quantum gravity and the renormalisation group , 2008, 0810.3675.

[20]  Christoph Rahmede,et al.  Investigating the ultraviolet properties of gravity with a Wilsonian renormalization group equation , 2008, 0805.2909.

[21]  Christoph Rahmede,et al.  ULTRAVIOLET PROPERTIES OF f(R)-GRAVITY , 2007, 0705.1769.

[22]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[23]  C. Wetterich,et al.  Exact evolution equation for the effective potential , 1993, 1710.05815.

[24]  Astrid Eichhorn,et al.  Ghost anomalous dimension in asymptotically safe quantum gravity , 2010, 1001.5033.

[25]  T. Plehn,et al.  Extra Dimensions and their Ultraviolet Completion , 2009, 0912.2653.

[26]  Off-diagonal coefficients of the DeWitt-Schwinger and Hadamard representations of the Feynman propagator , 2005, gr-qc/0511115.

[27]  M. Reuter,et al.  Quantum Einstein gravity: Towards an asymptotically safe field theory of gravity , 2007 .

[28]  Jan M. Pawlowski.  Aspects of the functional renormalisation group , 2007 .

[29]  M. Reuter,et al.  Flow equation of quantum Einstein gravity in a higher derivative truncation , 2002 .

[30]  D. Litim.  Fixed points of quantum gravity , 2003, hep-th/0312114.

[31]  M. Reuter,et al.  Is quantum Einstein gravity nonperturbatively renormalizable , 2002 .

[32]  R. Percacci.  Approaches to Quantum Gravity: Asymptotic safety , 2007, 0709.3851.

[33]  Tilman Plehn,et al.  Signatures of gravitational fixed points at the Large Hadron Collider. , 2007, Physical review letters.

[34]  Fixed points of quantum gravity in extra dimensions , 2006, hep-th/0602203.

[35]  Martin Reuter,et al.  Conformal sector of quantum Einstein gravity in the local potential approximation: Non-Gaussian fixed point and a phase of unbroken diffeomorphism invariance , 2008, 0804.1475.

[36]  D. Raine.  General relativity , 1980, Nature.

[37]  Martin Reuter,et al.  Nonperturbative evolution equation for quantum gravity , 1998 .

[38]  Martin Reuter,et al.  Background Independence and Asymptotic Safety in Conformally Reduced Gravity , 2008, 0801.3287.

[39]  D. Litim.  Optimized renormalization group flows , 2001, hep-th/0103195.

[40]  Frank Saueressig,et al.  On the Renormalization Group Flow of Gravity , 2007, 0712.0445.

[41]  Flow equations for the relevant part of the pure Yang—Mills action , 1995, hep-th/9506019.

[42]  C. Bervillier,et al.  Exact renormalization group equations. An Introductory review , 2000 .

[43]  Nonperturbative Faddeev-Popov formula and the infrared limit of QCD , 2003, hep-ph/0303028.

[44]  Reinhard Alkofer,et al.  The infrared behaviour of QCD Green's functions ☆: Confinement, dynamical symmetry breaking, and hadrons as relativistic bound states , 2000 .

[45]  M. Reuter,et al.  Fractal spacetime structure in asymptotically safe gravity , 2005 .

[46]  B. Koch,et al.  Renormalization group improved black hole space-time in large extra dimensions , 2009, 0912.4517.

[47]  Wataru Souma,et al.  Non-Trivial Ultraviolet Fixed Point in Quantum Gravity , 1999, hep-th/9907027.

[48]  S. Carlip.  Spontaneous Dimensional Reduction in Short‐Distance Quantum Gravity? , 2009, 0909.3329.

[49]  B. Koch.  Renormalization group and black hole production in large extra dimensions , 2007, 0707.4644.