arXiv subjects

A. Pernace

Publications and source records attributed to A. Pernace.

3 recordsLinked to original sources

arXiv2026

Hard cutoff and gauge theories

According to usual calculations, the use of a hard cutoff $\Lambda$ in gauge theories leads to a violation of gauge invariance. This seems to generate a tension between gauge theories and the Wilsonian effective field theory (EFT) paradigm, where $\Lambda$ has the physical meaning of ultimate scale of the theory, the scale above which the latter has to be replaced by its UV completion. In the present work, considering the Euler-Heisenberg correction to the free Maxwell action, we present a way to introduce the Wilsonian hard UV cutoff $\Lambda$ that preserves gauge invariance at the quantum level. For both scalar and fermionic QED, we recover the well-known Euler-Heisenberg result obtained within proper-time regularization, apart from terms that are generically cutoff-suppressed. These terms, periodic in the inverse background field, might become relevant in regimes where the latter probes scales not much smaller than $\Lambda$. On the theoretical side, the methods developed in the present work represent a first step towards a new (closer in spirit to the Wegner-Houghton construction) realization of the Wilsonian renormalization group program in gauge theories.

hep-th↗

arXiv2024

Path integral measure and RG equations for gravity

Considering the Einstein-Hilbert truncation for the running action in (euclidean) quantum gravity, we derive the renormalization group equations for the cosmological and Newton constant. We find that these equations admit only the Gaussian fixed point with a UV-attractive and a UV-repulsive eigendirection, and that there is no sign of the non-trivial UV-attractive fixed point of the asymptotic safety scenario. Crucial to our analysis is a careful treatment of the measure in the path integral that defines the running action and a proper introduction of the physical running scale $k$. We also show why and how in usual implementations of the RG equations the aforementioned UV-attractive fixed point is generated.

hep-th↗

arXiv2024

Path integral measure and cosmological constant

Considering (euclidean) quantum gravity in the Einstein-Hilbert truncation, we calculate the one-loop effective action $\Gamma^{1l}_{\rm grav}$ using a spherical background. Usually, this calculation is performed resorting to proper-time regularization within the heat kernel expansion and gives rise to quartically and quadratically UV-sensitive contributions to the vacuum energy $\rho_{\rm vac}=\frac{\Lambda_{\rm cc}}{8\pi G}$, with $\Lambda_{\rm cc}$ and $G$ cosmological and Newton constant, respectively. We show that, if the measure in the path integral that defines $\Gamma^{1l}_{\rm grav}$ is correctly taken into account, and the physical UV cutoff $\Lambda_{\rm cut}$ properly introduced, $\rho_{\rm vac}$ presents only a (mild) logarithmic sensitivity to $\Lambda_{\rm cut}$. We also consider a free scalar field and a free Dirac field on a spherical gravitational background, and find that the same holds true even in the presence of matter. These results are found without resorting to any supersymmetric embedding of the theory, and shed new light on the cosmological constant problem.

hep-th↗