Narrow Results

We analyze cylindrical gravitational waves in vacuo with general polarization and develop a viewpoint complementary to that presented recently by Niedermaier showing that the auxiliary sigma model associated with this family of waves is not renormalizable in the standard perturbative sense.

We study the fixed-point interactions and the renormalization group invariance for an effective nucleon–nucleon (NN) interaction in the leading-order (LO) chiral effective field theory (ChEFT) renormalized within the framework of the subtracted kernel method (SKM) approach. By solving a nonrelativistic Callan–Symanzik (NRCS) equation we show how the driving term evolves with the subtraction scale to keep the T-matrix invariant. We calculate the fixed-point interaction from the driving term and compare the results obtained with and without its evolution through the NRCS equation.

We discuss the renormalization procedure for quantum scalar fields with modified dispersion relations in curved spacetimes. We consider two different ways of introducing modified dispersion relations: through the interaction with a dynamical temporal vector field, as in the context of the Einstein–Aether theory, and breaking explicitly the covariance of the theory, as in Hǒrava–Lifshitz gravity. Working in the weak field approximation, we show that the general structure of the counterterms depends on the UV behavior of the dispersion relations and on the mechanism chosen to introduce them.

Quantum field theory on rotating black hole spacetimes is plagued with technical difficulties. Here, we describe a general method to renormalize and compute the vacuum polarization of a quantum field in the Hartle–Hawking state on rotating black holes. We exemplify the technique with a massive scalar field on the warped AdS₃ black hole solution to topologically massive gravity, a deformation of (2 + 1)-dimensional Einstein gravity. We use a "quasi-Euclidean" technique, which generalizes the Euclidean techniques used for static spacetimes, and we subtract the divergences by matching to a sum over mode solutions on Minkowski spacetime. This allows us, for the first time, to have a general method to compute the renormalized vacuum polarization, for a given quantum state, on a rotating black hole, such as the physically relevant case of the Kerr black hole in four dimensions.

In quantum-field theory in curved spacetime, two important physical quantities are the expectation value of the stress-energy tensor $〈{\widehat{T}}_{\mu \nu }〉$ and of the square of the field operator $〈{\widehat{\phi }}^2〉$. These expectation values must be renormalized, which is usually performed via the so-called point-splitting prescription. However, the renormalization method that is usually implemented in the literature, in principle, only applies to static, spherically-symmetric spacetimes, and does not readily generalize to other types of spacetime. We present a novel implementation of the renormalization procedure which may be used in the future for more general spacetimes, such as Kerr black hole spacetime. As an example, we apply our method to the renormalization of $〈{\widehat{\phi }}^2〉$ for a massless scalar field in Bertotti–Robinson spacetime.

We argue that quantum gravity is nonlocal, first by recalling well-known arguments that support this idea and then by focusing on a point not usually emphasized: that making a conventional effective field theory (EFT) for quantum gravity is particularly difficult, and perhaps impossible in principle. This inability to realize an EFT comes down to the fact that gravity itself sets length scales for a problem: when integrating out degrees of freedom above some cutoff, the effective metric one uses will be different, which will itself re-define the cutoff. We also point out that even if the previous problem is fixed, naïvely applying EFT in gravity can lead to problems — we give a particular example in the case of black holes.

In this paper, we consider the nature of the cosmological constant as due by quantum fluctuations. Quantum fluctuations are generated at Planckian scales by noncommutative effects and watered down at larger scales up to a decoherence scale $L_D$, where classicality is reached. In particular, we formally depict the presence of the scale at $L_D$ by adopting a renormalization group approach. As a result, an analogy arises between the expression for the observed cosmological constant $\overline{\mathrm{\Lambda }}$ generated by quantum fluctuations and the one expected by a renormalization group approach, provided that the renormalization scale $\mu$ is suitably chosen. In this framework, the decoherence scale $L_D$ is naturally identified with the value ${\mu }_D$ with $\hslash {\mu }_D$ representing the minimum allowed particle-momentum for our visible universe. Finally, by mimicking renormalization group approach, we present a technique to formally obtain a nontrivial infrared (IR) fixed point at $\mu ={\mu }_D$ in our model.