RG flows of Quantum Einstein Gravity in the linear-geometric approximation

Demmel, Maximilian; Saueressig, Frank; Zanusso, Omar

doi:10.1016/j.aop.2015.04.018

Cited by 70 publications

(102 citation statements)

References 143 publications

(304 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…So when we go through the usual procedure and define the associated EAA, the derivation of ∂ k Γ k ≥ 0 in the main part of this paper applies to it, provided the above exact compensation of the ghost and V µ contributions persists in presence of an IR cutoff. While this is not the case for a generic cutoff, it has been shown [92] that if the cutoff operators R k of the ghost and metric fluctuations, respectively, are appropriately related, which always can be achieved, the compensation does indeed persist. For further details the reader is referred to [92].…”

Section: Jhep03(2015)065mentioning

confidence: 98%

“…While this is not the case for a generic cutoff, it has been shown [92] that if the cutoff operators R k of the ghost and metric fluctuations, respectively, are appropriately related, which always can be achieved, the compensation does indeed persist. For further details the reader is referred to [92]. Thus we have shown that (at the very least) when the ghosts are the only Grassmannodd fields it is in principle always possible to set up the gauge fixing and ghost sector of the EAA and its FRGE in such a way that ∂ k Γ k ≥ 0 holds true pointwise.…”

Section: Jhep03(2015)065mentioning

confidence: 98%

See 1 more Smart Citation

Towards a C-function in 4D quantum gravity

Becker

Reuter

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

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 dimensions. It becomes stationary both at critical points and in classical regimes, and decreases monotonically along RG trajectories provided the breaking of the split-symmetry which relates background and quantum fields is sufficiently weak. Within the Asymptotic Safety approach we test the proposal for Quantum Einstein Gravity in d > 2 dimensions, performing detailed numerical investigations in d = 4. We find that the bi-metric EinsteinHilbert truncation of theory space introduced recently is general enough to yield perfect monotonicity along the RG trajectories, while its more familiar single-metric analog fails to achieve this behavior which we expect on general grounds. Investigating generalized crossover trajectories connecting a fixed point in the ultraviolet to a classical regime with positive cosmological constant in the infrared, the C -function is shown to depend on the choice of the gravitational instanton which constitutes the background spacetime. For de Sitter space in 4 dimensions, the Bekenstein-Hawking entropy is found to play a role analogous to the central charge in conformal field theory. We also comment on the idea of a 'Λ-N connection' and the 'N -bound' discussed earlier.

show abstract

Section: Jhep03(2015)065mentioning

confidence: 98%

Section: Jhep03(2015)065mentioning

confidence: 98%

Towards a C-function in 4D quantum gravity

Becker

Reuter

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

show abstract

“…Finally, the total Wilsonian effective action can be written 17) and C k (p) is an ultraviolet cutoff profile for this effective action and effective partition function, which regularises at scale k. C k (p) has to satisfy the same conditions asC Λ (p) above (with the replacement Λ → k of course). Since the functional integral with this action S tot,k is therefore already completely regularised in the ultraviolet, there is no need for any dependence on the overall UV cutoff Λ.…”

Section: Jhep11(2015)094mentioning

confidence: 99%

“…[2], there is a wealth of literature investigating asymptotic safety in this way. For reviews and introductions see [10][11][12][13][14], and for recent advances see for example [15][16][17][18][19][20][21][22][23][24]. In the vast majority of this work the RG flow equation takes the generic form [3]:…”

Section: Introductionmentioning

confidence: 99%

Solutions to the reconstruction problem in asymptotic safety

Morris

Slade

2015

J. High Energ. Phys.

View full text Add to dashboard Cite

Starting from a full renormalised trajectory for the effective average action (a.k.a. infrared cutoff Legendre effective action) Γ k , we explicitly reconstruct corresponding bare actions, formulated in one of two ways. The first step is to construct the corresponding Wilsonian effective action S k through a tree-level expansion in terms of the vertices provided by Γ k . It forms a perfect bare action giving the same renormalised trajectory. A bare action with some ultraviolet cutoff scale Λ and infrared cutoff k necessarily produces an effective average action Γ Λ k that depends on both cutoffs, but if the already computed S Λ is used, we show how Γ Λ k can also be computed from Γ k by a tree-level expansion, and that Γ Λ k → Γ k as Λ → ∞. Along the way we show that Legendre effective actions with different UV cutoff profiles, but which correspond to the same Wilsonian effective action, are related through tree-level expansions. All these expansions follow from Legendre transform relationships that can be derived from the original one between Γ Λ k and S k .

show abstract

“…However this is also an area where there is little guidance from current experimental observation or other techniques, and therefore one must place particular reliance on a rigorous understanding of the mathematical structure that the exact RG exposes, in so far as this is possible. This is especially so with recent work on "functional truncations" [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36].…”

Section: Introductionmentioning

confidence: 99%

Fate of nonpolynomial interactions in scalar field theory

Bridle

Morris

2016

Phys. Rev. D

View full text Add to dashboard Cite

We present an exact RG (renormalization group) analysis of O(N )-invariant scalar field theory about the Gaussian fixed point. We prove a series of statements that taken together show that the non-polynomial eigen-perturbations found in the LPA (local potential approximation) at the linearised level, do not lead to new interactions, i.e. enlarge the universality class, neither in the LPA or treated exactly. Non-perturbatively, their RG flow does not emanate from the fixed point. For the equivalent Wilsonian effective action they can be re-expressed in terms of the usual couplings to polynomial interactions, which can furthermore be tuned to be as small as desired for all finite RG time. For the infrared cutoff Legendre effective action, this can also be done for the infrared evolution. We explain why this is nevertheless consistent with the fact that the large field behaviour is fixed by these perturbations.arXiv:1605.06075v3 [hep-th]

show abstract

RG flows of Quantum Einstein Gravity in the linear-geometric approximation

Cited by 70 publications

References 143 publications

Towards a C-function in 4D quantum gravity

Towards a C-function in 4D quantum gravity

Solutions to the reconstruction problem in asymptotic safety

Fate of nonpolynomial interactions in scalar field theory

Contact Info

Product

Resources

About