arXiv subjects

John F. Donoghue

Publications and source records attributed to John F. Donoghue.

At least 19 recordsLinked to original sources

arXiv2025

Higher Derivative Sigma Models

We explore the nature of running couplings in the higher derivative linear and nonlinear sigma models and show that the results in dimensional regularization for the physical running couplings do not always match the values quoted in the literature. Heat kernel methods identify divergences correctly, but not all of these divergences are related to physical running couplings. Likewise the running found using the Functional Renormalization Group does not always appear as running couplings in physical processes, even for the case of logarithmic running. The basic coupling of the higher derivative SU(N) nonlinear sigma model does not run at all at one loop, in contrast to published claims for asymptotic freedom. At one loop we describe how to properly identify the physical running couplings in these theories, and provide revised numbers for the higher derivative nonlinear sigma model.

hep-th↗

arXiv2025

Visions in Quantum Gravity

To deepen our understanding of Quantum Gravity and its connections with black holes and cosmology, building a common language and exchanging ideas across different approaches is crucial. The Nordita Program "Quantum Gravity: from gravitational effective field theories to ultraviolet complete approaches" created a platform for extensive discussions, aimed at pinpointing both common grounds and sources of disagreements, with the hope of generating ideas and driving progress in the field. This contribution summarizes the twelve topical discussions held during the program and collects individual thoughts of speakers and panelists on the future of the field in light of these discussions.

hep-th↗

arXiv2024

Do $Λ_{CC}$ and $G$ run?

No. In this brief pedagogic note, I describe why the cosmological constant and Newton's constant are not running parameters in physical reactions.

hep-th↗

arXiv2024

Amplitudes and Renormalization Group Techniques: A Case Study

We explore the properties of a simple renormalizable shift symmetric model with a higher derivative kinetic energy and quartic derivative coupling, that can serve as a toy model for higher derivative theories of gravity. The scattering amplitude behaves as in a normal effective field theory below the threshold for the production of ghosts, but has an unexpectedly soft behavior above the threshold. The physical running of the parameters is extracted from the 2-point and 4-point amplitudes. The results are compared to those obtained by other methods and are found to agree only in limiting cases. We draw several lessons that may apply also to gravity.

hep-th↗

arXiv2024

Renormalization and running in the 2D $CP(1)$ model

We calculate the scattering amplitude in the two dimensional $CP(1)$ model in a regularization scheme independent way. When using cutoff regularization, a new Feynman rule from the path integral measure is required if one is to preserve the symmetry. The physical running of the coupling with renormalization scale arises from a UV finite Feynman integral in all schemes. We reproduce the usual result with asymptotic freedom, but the pathway to obtaining the beta function can be different in different schemes. We also comment on the way that this model evades the classic argument by Landau against asymptotic freedom in non-gauge theories.

hep-th↗

arXiv2024

Physical running of couplings in quadratic gravity

We argue that the well-known beta functions of quadratic gravity do not correspond to the physical dependence of scattering amplitudes on external momenta, and derive the correct physical beta functions. Asymptotic freedom turns out to be compatible with the absence of tachyons.

hep-th↗

arXiv2023

Quantum General Relativity and Effective Field Theory

This is a review of some of the concepts and results of the effective field theory treatment of quantum general relativity. Included are lessons of low energy quantum gravity, and a discussion of the limits of effective field theory techniques.

hep-th↗

arXiv2022

Non-local partner to the cosmological constant

I show that quantum corrections due to a massive particle generates a non-local term in the gravitational effective action which is of zeroth order in the derivative expansion, much like the cosmological constant. It carries a fixed coefficient which is very much larger than the cosmological constant, and which cannot be fine-tuned. The interaction is active at scales above the particle's mass. This is of the form $m^4 (\frac1{\Box}R)_x " " (\frac1{\Box}R)_y$, and I discuss the meaning of $ " " $ and other aspects of its interpretation.

hep-th↗

arXiv2021

On Quadratic Gravity

We provide a brief overview of what is known about Quadratic Gravity, which includes terms quadratic in the curvatures in the fundamental action. This is proposed as a renormalizeable UV completion for quantum gravity which continues to use the metric as the fundamental dynamical variable. However, there are unusual field-theoretic consequences because the propagators contain quartic momentum dependence. At the present stage of our understanding, Quadratic Gravity continues to be a viable candidate for a theory of quantum gravity.

hep-th↗

arXiv2021

Causality and gravity

We show how uncertainty in the causal structure of field theory is essentially inevitable when one includes quantum gravity. This includes the fact that lightcones are ill-defined in such a theory. This effect is small in the effective field theory regime, where it it independent of the UV completion of the theory, but grows with energy and represents an unknown uncertainty for a generic UV completion. We include details of the causality uncertainty which arises in a particular UV completion, i.e. quadratic gravity. We describe how the mechanisms uncovered in the effective field theory treatment, and some of those in quadratic gravity, could be common features of quantum gravity.

hep-th↗

arXiv2021

The cosmological constant and the use of cutoffs

Of the contributions to the cosmological constant, zero-point energy and self energy contributions scale as $Λ^4$ where $Λ$ is an ultraviolet cutoff used to regulate the calculations. I show that such contributions vanish when calculated in perturbation theory. This demonstration uses a little-known modification to perturbation theory found by Honerkamp and Meetz and by Gerstein, Jackiw, Lee and Weinberg which comes into play when using cutoffs and interactions with multiple derivatives, as found in chiral theories and gravity. In a path integral treatment, the new interaction arises from the path integral measure. This reduces the sensitivity of the cosmological constant to the high energy cutoff significantly, although it does not resolve the cosmological constant problem. The feature removes one of the common motivations for supersymmetry. It also calls into question some of the results of the Asymptotic Safety program. Covariance and quadratic cutoff dependence are also briefly discussed.

hep-th↗

arXiv2020

Quantum causality and the arrows of time and thermodynamics

In the understanding of the fundamental interactions, the origin of an arrow of time is viewed as problematic. However, quantum field theory has an arrow of causality, which tells us which time direction is the past lightcone and which is the future. This direction is tied to the conventions used in the quantization procedures. The different possible causal directions have related physics - in this sense they are covariant under time-reversal. However, only one causal direction emerges for a given set of conventions. This causal arrow tells us the direction that scattering reactions proceed. The time direction of scattering in turn tells us the time direction for which entropy increases - the so-called arrow of thermodynamics. This connection is overlooked in most discussions of the arrow of time.

quant-ph↗

arXiv2020

A Critique of the Asymptotic Safety Program

The present practice of Asymptotic Safety in gravity is in conflict with explicit calculations in low energy quantum gravity. This raises the question of whether the present practice meets the Weinberg condition for Asymptotic Safety. I argue, with examples, that the running of $Λ$ and $G$ found in Asymptotic Safety are not realized in the real world, with reasons which are relatively simple to understand. A comparison/contrast with quadratic gravity is also given, which suggests a few obstacles that must be overcome before the Lorentzian version of the theory is well behaved. I make a suggestion on how a Lorentzian version of Asymptotic Safety could potentially solve these problems.

hep-th↗

arXiv2019

Gravitons and Pions

Both gravitons and pions are described by non-linear and non-renormalizable actions at low energies. These are most usefully treated by effective field theory, which is a full quantum field theoretic approach that relies only on the low energy degrees of freedom and their interactions. The gravitational case is particularly clean because of the masslessness of the graviton and the wide separation of scales. This essay provides an overview of this approach.

nucl-th↗

arXiv2019

Unitarity, stability and loops of unstable ghosts

We present a new understanding of the unstable ghost-like resonance which appears in theories such as quadratic gravity and Lee-Wick type theories. Quantum corrections make this resonance unstable, such that it does not appear in the asymptotic spectrum. We prove that these theories are unitary to all orders. Unitarity is satisfied by the inclusion of only cuts from stable states in the unitarity sum. This removes the need to consider this as a ghost state in the unitarity sum. However, we often use a narrow-width approximation where we do include cuts through unstable states, and ignore cuts through the stable decay products. If we do this with the unstable ghost resonance at one loop, we get the correct answer only by using a contour which was originally defined by Lee and Wick. The quantum effects also provide damping in both the Feynman and the retarded propagators, leading to stability under perturbations.

hep-th↗

arXiv2019

The arrow of causality and quantum gravity

Causality in quantum field theory is defined by the vanishing of field commutators for space-like separations. However, this does not imply a direction for causal effects. Hidden in our conventions for quantization is a connection to the definition of an arrow of causality, i.e. what is the past and what is the future. If we mix quantization conventions within the same theory, we get a violation of microcausality. In such a theory with mixed conventions the dominant definition of the arrow of causality is determined by the stable states. In some quantum gravity theories, such as quadratic gravity and possibly asymptotic safety, such a mixed causality condition occurs. We discuss some of the implications.

hep-th↗

arXiv2019

Massive poles in Lee-Wick quantum field theory

Most discussions of propagators in Lee-Wick theories focus on the presence of two massive complex conjugate poles in the propagator. We show that there is in fact only one pole near the physical region, or in another representation three pole-like structures with compensating extra poles. The latter modified Lehmann representation is useful caculationally and conceptually only if one includes the resonance structure in the spectral integral.

hep-th↗

arXiv2018

Gauge Assisted Quadratic Gravity: A Framework for UV Complete Quantum Gravity

We discuss a variation of quadratic gravity in which the gravitational interaction remains weakly coupled at all energies, but is assisted by a Yang-Mills gauge theory which becomes strong at the Planck scale. The Yang-Mills interaction is used to induce the usual Einstein-Hilbert term, which was taken to be small or absent in the original action. We study the spin-two propagator in detail, with a focus on the high mass resonance which is shifted off the real axis by the coupling to real decay channels. We calculate scattering in the $J=2$ partial wave and show explicitly that unitarity is satisfied. The theory will in general have a large cosmological constant and we study possible solutions to this, including a unimodular version of the theory. Overall, the theory satisfies our present tests for being a ultraviolet completion of quantum gravity.

hep-th↗