Computing the effective action with the functional renormalization group

Codello, Alessandro; Percacci, Roberto; Rachwał, Lesław; Tonero, Alberto

doi:10.1140/epjc/s10052-016-4063-3

Cited by 49 publications

(58 citation statements)

References 93 publications

(124 reference statements)

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“…The form factor may be used only as a way to interpolate between infrared (IR) and UV behavior of the theory in a covariant way. Such ideas are similar to the ideas of the smooth covariant cutoff developed in the field of functional RG [11][12][13][14][15][16]. We believe that the true significance of the form factors used in nonlocal theories will be revealed only at the loop level.…”

Section: Jhep08(2015)038mentioning

confidence: 53%

Scattering amplitudes in super-renormalizable gravity

Donà

Giaccari

Modesto

et al. 2015

J. High Energ. Phys.

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We explicitly compute the tree-level on-shell four-graviton amplitudes in four, five and six dimensions for local and weakly nonlocal gravitational theories that are quadratic in both, the Ricci and scalar curvature with form factors of the d'Alembertian operator inserted between. More specifically we are interested in renormalizable, superrenormalizable or finite theories. The scattering amplitudes for these theories turn out to be the same as the ones of Einstein gravity regardless of the explicit form of the form factors. As a special case the four-graviton scattering amplitudes in Weyl conformal gravity are identically zero. Using a field redefinition, we prove that the outcome is correct for any number of external gravitons (on-shell n−point functions) and in any dimension for a large class of theories. However, when an operator quadratic in the Riemann tensor is added in any dimension (with the exception of the Gauss-Bonnet term in four dimensions) the result is completely altered, and the scattering amplitudes depend on all the form factors introduced in the action.

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Section: Jhep08(2015)038mentioning

confidence: 53%

Scattering amplitudes in super-renormalizable gravity

Donà

Giaccari

Modesto

et al. 2015

J. High Energ. Phys.

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“…in which ∆ = −∂ 2 x is the Laplacian operator in flat space and F µν = ∂ µ A ν − ∂ ν A µ is the Abelian curvature tensor [37]. It should be clear that the non-local form-factor appearing between the two copies of F µν is a covariant way of writing (1) in which the momentum scale q 2 comes from Fourier transformation of the differential operator ∆.…”

Section: Mass-dependent Schemesmentioning

confidence: 99%

Vacuum Effective Actions and Mass-Dependent Renormalization in Curved Space

2019

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We review past and present results on the non-local form-factors of the effective action of semiclassical gravity in two and four dimensions computed by means of a covariant expansion of the heat kernel up to the second order in the curvatures. We discuss the importance of these form-factors in the construction of mass-dependent beta functions for the Newton's constant and the other gravitational couplings.

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“…For the aim of this paper it is relevant that there is no renormalization of the Newton constant (β G N = 0). For the case of Minkowski signature, one more reason to use DR is that the cut-off regularization scheme is not naively Lorentz invariant (see however [65] for a different point of view). As we noticed above, the cancellation of some beta functions is actually automatically valid for perturbations of gravity around a background that is a classical solution of (9) (in particular a Ricci-flat one).…”

Section: Divergences In Dimensional Regularization Schemementioning

confidence: 99%

“…This statistical interpretation is quite natural in the case of physical regulators, like cut-off by a UV scale e.g., but when gravity is involved, covariant regulators, such as Pauli-Villars [65,71] and the heat kernel regularization, should be preferred and there is no obvious way of carrying out such a counting. This has led to attempts to distinguish statistical and conical definitions of entropy, arguing that the latter is marred by such unphysical features as not being positive definite and being gauge-and regulator-dependent [8].…”

Section: Conical Entropymentioning

confidence: 99%

Finite entanglement entropy of black holes

et al. 2018

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We compute the area term contribution to black holes' entanglement entropy (using the conical technique) for a class of local or weakly non-local super-renormalizable gravitational theories coupled to matter. For the first time, we explicitly prove that all the beta functions in the proposed theory, except for the cosmological constant, are identically zero in cut-off regularization scheme and not only in dimensional regularization scheme. In particular, we show that there is no divergence quadratic in cut-off and hence there is no contribution to the beta function of the Newton constant. As a consequence of this result, we argue that in these theories of gravity conical entropy is a sensible definition of physical entropy, in particular, it is positive-definite and gauge independent. On top of this the conical entropy, being expressed only in terms of the classical Newton constant, turns out to be finite and naturally coincides with Bekenstein-Hawking entropy. Finally, we propose a theory in which the renormalization of the Newton constant is entirely due to the Standard Model matter, arguing that such a contribution does not give the usual interpretational problems of conical entropy discussed in the literature.

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Computing the effective action with the functional renormalization group

Cited by 49 publications

References 93 publications

Scattering amplitudes in super-renormalizable gravity

Scattering amplitudes in super-renormalizable gravity

Vacuum Effective Actions and Mass-Dependent Renormalization in Curved Space

Finite entanglement entropy of black holes

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