On the non-local heat kernel expansion

Codello, Alessandro; Zanusso, Omar

doi:10.1063/1.4776234

Cited by 68 publications

(104 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In two dimensions the Ricci tensor is proportional to the Ricci scalar R µν = 1 2 g µν R so there is only one non-local heat kernel structure function at the order curvature square [10] and this is given by the following linear combination:…”

Section: λmentioning

confidence: 99%

“…the beta functions are the coefficients of the expansion of the functional trace on the rhs of the flow equation. In the context of quantum gravity, the expansion of the functional trace is performed with the fundamental aid of the heat kernel expansion, in both its local and non-local realizations [10]. These techniques allow us to work covariantly at any step of the computations.…”

Section: Flow Equationsmentioning

confidence: 99%

“…in which s is the diffusion time, and K s = e −s∆ is the heat kernel, which is a solution of the heat equation [10]:…”

Section: Fractal Properties Of Spacetimementioning

confidence: 99%

See 2 more Smart Citations

Scaling and renormalization in two dimensional quantum gravity

Codello

D'Odorico

2015

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

We study scaling and renormalization in two dimensional quantum gravity in a covariant framework. After reviewing the definition of a proper path integral measure, we use scaling arguments to rederive the KPZ relations, the fractal dimension of the theory and the scaling of the reparametrization-invariant two point function. Then we compute the scaling exponents entering in these relations by means of the functional RG. We show that a key ingredient to obtain the correct results already known from Liouville theory is the use of the exponential parametrization for metric fluctuations. We also show that with this parametrization we can recover the correct finite part of the effective action as the ǫ → 0 limit of quantum gravity in d = 2 + ǫ.

show abstract

Section: λmentioning

confidence: 99%

Section: Flow Equationsmentioning

confidence: 99%

See 1 more Smart Citation

Scaling and renormalization in two dimensional quantum gravity

Codello

D'Odorico

2015

Phys. Rev. D

Self Cite

View full text Add to dashboard Cite

show abstract

“…Comparing (10) with the stand expansion of g µν used in perturbation theory, g µν = δ µν + √ 16πG N h µν with G N being Newton's constant, identifies the natural scale for Λ as the Planck mass m Pl = (8πG N ) −1/2 (also see [64] for a related discussion). A lengthy but in principle straightforward calculation [31,32,[60][61][62] then yields the expression for the inverse propagators of the physical fields including the full-momentum dependence…”

Section: The Spectral Action and Its Bosonic Propagatorsmentioning

confidence: 99%

Spectral dimensions from the spectral action

2015

Self Cite

View full text Add to dashboard Cite

The generalised spectral dimension DS(T ) provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative geometry. Analysing the propagation of spin-0, spin-1 and spin-2 fields, we show that a non-trivial spectral dimension arises already at the classical level. The effective field theory interpretation of the spectral action yields plateaustructures interpolating between a fixed spin-independent DS(T ) = dS for short and DS(T ) = 4 for long diffusion times T . Going beyond effective field theory the spectral dimension is completely dominated by the high-momentum properties of the spectral action, yielding DS(T ) = 0 for all spins. Our results support earlier claims that high-energy bosons do not propagate.

show abstract

“…For an alternative derivation see [25]. Keeping terms up to second order in the fields strengths, the non-local heat kernel expansion reads as follows:…”

Section: The Non-local Heat Kernel Expansionmentioning

confidence: 99%

Computing the effective action with the functional renormalization group

et al. 2016

Self Cite

View full text Add to dashboard Cite

The "exact" or "functional" renormalization group equation describes the renormalization group flow of the effective average action k . The ordinary effective action 0 can be obtained by integrating the flow equation from an ultraviolet scale k = down to k = 0. We give several examples of such calculations at one-loop, both in renormalizable and in effective field theories. We reproduce the four-point scattering amplitude in the case of a real scalar field theory with quartic potential and in the case of the pion chiral Lagrangian. In the case of gauge theories, we reproduce the vacuum polarization of QED and of Yang-Mills theory. We also compute the two-point functions for scalars and gravitons in the effective field theory of scalar fields minimally coupled to gravity.

show abstract

On the non-local heat kernel expansion

Cited by 68 publications

References 29 publications

Scaling and renormalization in two dimensional quantum gravity

Scaling and renormalization in two dimensional quantum gravity

Spectral dimensions from the spectral action

Computing the effective action with the functional renormalization group

Contact Info

Product

Resources

About