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No. In this brief pedagogic note, I describe why the cosmological constant and Newton's constant are not running parameters in physical reactions., Comment: An elaboration of some material presented at the 64th Cracow School of Theoretical Physics (2024). Accepted for publication in Acta Physica Polonica. 11 pages, 2 figures

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., Comment: Collection of summaries of twelve topical panel discussions and individual thoughts of speakers and panelists, Nordita Scientific Program "Quantum Gravity: from gravitational EFTs to UV complete approaches". 62 pages + references, no figures

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., Comment: 11 pages, 1 figure

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., Comment: 8 pages, 2 figures, 2 tables; v2: Some modifications throughout the text. Revised version as accepted by PRL

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., Comment: 19 pages, 1 figure

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., Comment: 20 pages, 2 figures

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., Comment: 27 Pages. Invited chapter for the Section "Effective Quantum Gravity" of the "Handbook of Quantum Gravity" (Eds. C. Bambi, L. Modesto and I.L. Shapiro, Springer Singapore, expected in 2023) Typos corrected

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., Comment: 10 pages, 1 figure, comments and relevant references have been added

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., Comment: 9 pages. This is a distant reflection of a talk given by JFD at the online workshop on Quantum Gravity, Higher Derivatives and Nonlocality, and is to be published in a special volume for the workshop

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., Comment: 15 pages, 3 figures, revised version as accepted by JHEP

In theories with higher time derivatives, the Hamiltonian analysis of Ostrogradsky predicts an instability. However, this Hamiltonian treatment does not correspond the way that these theories are treated in quantum field theory, and the instability may be avoided in at least some cases. We present a very simple model which illustrates these features., Comment: 11 pages, 2 figures Some references and comments added

Of the contributions to the cosmological constant, zero-point energy and self energy contributions scale as $\Lambda^4$ where $\Lambda$ 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., Comment: 9 pages, 1 figure Reference to Fradkin - Vilkovisky added, as well as some clarifying comments

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., Comment: This second version has a re-ordered and expanded discussion (to enhance the QFT perspective) and two new sections. The title is slightly changed. This is the version which was published in Progress in Particle and Nuclear Physics, Vol 115, 103812 (2020). 15 pages, 2 figures

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 $\Lambda$ 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., Comment: 40 pages, 1 figure. Final version as published

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., Comment: 8 pages, 3 figures. Accepted for publication in a special topical issue of the European Journal of Phyiscs A, "The tower of effective (field) theories and the emergence of nuclear phenomena"

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., Comment: 5 pages, 2 figures

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., Comment: 24 pages, 12 figures, some typos corrected and a discussion of related work improved

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., Comment: 10 pages, 8 figures. Version 2 has an improved drawing of Fig. 3

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., Comment: 22 pages, 3 figures

We evaluate the induced value of Newton's constant which would arise in QCD. The ingredients are modern lattice results, perturbation theory and the operator product expansion. The resulting shift in the Planck mass is positive. A scaled-up version of such a theory may be part of a quantum field theory treatment of gravity., Comment: 11 pages, one figure, references added, revised version as accepted for publication

The interactions of gravitons with spin-1 matter are calculated in parallel with the well known photon case. It is shown that graviton scattering amplitudes can be factorized into a product of familiar electromagnetic forms, and cross sections for various reactions are straightforwardly evaluated using helicity methods. Universality relations are identified. Extrapolation to zero mass yields scattering amplitudes for photon-graviton and graviton-graviton scattering. The phenomenon of light bending near a massive object, which is generally treated using classical general relativity, is discussed from alternative points of view., Comment: latex. 35 pages. 5 figures. Contribution written for the proceedings of the conference "Recent Developments in Strings and Gravity", Corfu 2016

Many arguments against quartic propagators, negative norm states and related effects concern the sicknesses which occur when the spectrum of the free particle Hamiltonian is formed. However, if the theory is more complicated, for example involving confinement such that the particle in question does not appear in the physical spectrum, those considerations do not apply directly. Path integral methods suggest that some of these may be acceptable theories. I provide an example that should be able to be simulated on a lattice which then allows a non-perturbative resolution of this question. In its SU(2) version it involves a scalar triplet with a quartic derivative Lagrangian coupled to the SU(2) gauge field. If this is verified to be a healthy theory, it could open new avenues in model building. I also discuss how strong interactions can dynamically modify the dispersion relation leaving a healthy effective field theory, using conformal gravity coupled to a Yang-Mills theory as an example. Such a theory could possibly form a UV completion for quantum gravity., Comment: 9 pages - some added references

These notes are an introduction to General Relativity as a Quantum Effective Field Theory, following the material given in a short course on the subject at EPFL. The intent is to develop General Relativity starting from a quantum field theoretic viewpoint, and to introduce some of the techniques needed to understand the subject., Comment: 70 pages

We consider scattering in quantum gravity and derive long-range classical and quantum contributions to the scattering of light-like bosons and fermions (spin-0, spin-1/2, spin-1) from an external massive scalar field, such as the Sun or a black hole. This is achieved by treating general relativity as an effective field theory and identifying the non-analytic pieces of the one-loop gravitational scattering amplitude. It is emphasized throughout the paper how modern amplitude techniques, involving spinor-helicity variables, unitarity, and squaring relations in gravity enable much simplified computations. We directly verify, as predicted by general relativity, that all classical effects in our computation are universal (in the context of matter type and statistics). Using an eikonal procedure we confirm the post-Newtonian general relativity correction for light-like bending around large stellar objects. We also comment on treating effects from quantum hbar dependent terms using the same eikonal method., Comment: latex 31 pages. 5 feynmp figures. v2: Clarifications on conventions and notations. Minors changes and latex format update. v3: A sign mistake corrected and various typos corrected

In the description of general covariance, the vierbein and the Lorentz connection can be treated as independent fundamental fields. With the usual gauge Lagrangian, the Lorentz connection is characterized by an asymptotically free running coupling. When running from high energy, the coupling gets large at a scale which can be called the Planck mass. If the Lorentz connection is confined at that scale, the low energy theory can have the Einstein Lagrangian induced at low energy through dimensional transmutation. However, in general there will be new divergences in such a theory and the Lagrangian basis should be expanded. I construct a conformally invariant model with a larger basis size which potentially may have the same property., Comment: 15 pages - corrected typos, updated references, small changes in discussion

The spin connection enters the theory of gravity as a nonabelian gauge field associated with local Lorentz transformations. Normally it is eliminated from making an extra assumption - that of the metricity of the vierbein field. However, treated by itself with the usual gauge action, it has a negative beta function, implying that it is asymptotically free. I suggest that the spin connection could be confined (or perhaps partially confined) in the same way as other nonabelian gauge fields. This would remove the need to make the extra assumption of metricity, as the spin connection would not be present in the low energy theory, leaving the symmetry to be realized only using metric variables., Comment: 6 pages - some new references, Euclidean discussion enhanced and partial-Euclidean discussion removed

The possibility of fundamental theories with very many ground states, each with different physical parameters, changes the way that we approach the major questions of particle physics. Most importantly, it raises the possibility that these different parameters could be realised in different domains in the larger universe. In this review, we survey the motivations for the multiverse and impact of the idea of the multiverse on the search for new physics beyond the Standard Model., Comment: Invited review for Annual Reviews of Nuclear and Particle Science, 37 pages

We explore the properties of non-local effective actions which include gravitational couplings. Non-local functions originally defined in flat space can not be easily generalized to curved space. The problem is made worse by the calculational impossibility of providing closed form expressions in a general metric. The technique of covariant perturbation theory (CPT) has been pioneered by Vilkovisky, Barvinsky and collaborators whereby the effective action is displayed as an expansion in the generalized curvatures similar to the Schwinger-De Witt local expansion. We present an alternative procedure to construct the non-local action which we call {\em non-linear completion}. Our approach is in one-to-one correspondence with the more familiar diagrammatic expansion of the effective action. This technique moreover enables us to decide on the appropriate non-local action that generates the QED trace anomaly in 4$D$. In particular we discuss carefully the curved space generalization of $\ln \Box$, and show that the anomaly requires both the anomalous logarithm as well as $1/\Box$ term where the latter is related to the Riegert anomaly action.

In this survey, we review some of the low energy quantum predictions of General Relativity which are independent of details of the yet unknown high-energy completion of the gravitational interaction. Such predictions can be extracted using the techniques of effective field theory., Comment: Invited Topical Review for J. Phys. G, 35 pages

We show how modern methods can be applied to quantum gravity at low energy. We test how quantum corrections challenge the classical framework behind the Equivalence Principle, for instance through introduction of non-locality from quantum physics, embodied in the Uncertainty Principle. When the energy is small we now have the tools to address this conflict explicitly. Despite the violation of some classical concepts, the EP continues to provide the core of the quantum gravity framework through the symmetry - general coordinate invariance - that is used to organize the effective field theory., Comment: 5 pages, Honorable Mention in the Gravity Research Foundation Essay Competition 2015

We discuss the derivation of the trace anomaly using a non-local effective action at one loop. This provides a simple and instructive form and emphasizes infrared physics. We then use this example to explore several of the properties of non-local actions, including displaying the action for the full non-local energy-momentum tensor. As an application, we show that the long-distance corrections at one loop lead to quantum violations of some classical consequences of the equivalence principle, for example producing a frequency dependence of the gravitational bending of light., Comment: 17 pages, 4 figures

We consider the scattering of lightlike matter in the presence of a heavy scalar object (such as the Sun or a Schwarzschild black hole). By treating general relativity as an effective field theory we directly compute the nonanalytic components of the one-loop gravitational amplitude for the scattering of massless scalars or photons from an external massive scalar field. These results allow a semiclassical computation of the bending angle for light rays grazing the Sun, including long-range $\hbar$ contributions. We discuss implications of this computation, in particular the violation of some classical formulations of the equivalence principle., Comment: 5 pages, 1 figure, v2: typos corrected, version to be published in PRL, v3: signs corrected

We derive the Regge behavior for the forward scattering amplitude in scalar field theory using the method of regions. We find that the leading Regge behavior to all orders can be obtained. Regge physics emerges from a kinematic region that involves the overlap of several modes, so that a careful treatment of the overlap regions is important. The most consistent and efficient approach utilizes graphs containing collinear, anti-collinear and Glauber modes, or modes of SCET_G, Comment: 18 pages, 6 figures

We discuss cosmological effects of the quantum loops of massless particles, which lead to temporal non-localities in the equations of motion governing the scale factor a(t). For the effects discussed here, loops cause the evolution of a(t) to depend on the memory of the curvature in the past with a weight that scales initially as 1/(t-t'). As one of our primary examples we discuss the situation with a large number of light particles, such that these effects occur in a region where gravity may still be treated classically. However, we also describe the effect of quantum graviton loops and the full set of Standard Model particles. We show that these effects decrease with time in an expanding phase, leading to classical behavior at late time. In a contracting phase, within our approximations the quantum results can lead to a bounce-like behavior at scales below the Planck mass, avoiding the singularities required classically by the Hawking-Penrose theorems. For conformally invariant fields, such as the Standard Model with a conformally coupled Higgs, this result is purely non-local and parameter independent., Comment: 18 pages, 13 figures - extra references added and minor wording changes

We compute the leading post-Newtonian and quantum corrections to the Coulomb and Newtonian potentials using the full modern arsenal of on-shell techniques; we employ spinor-helicity variables everywhere, use the Kawai-Lewellen-Tye (KLT) relations to derive gravity amplitudes from gauge theory and use unitarity methods to extract the terms needed at one-loop order. We stress that our results are universal and thus will hold in any quantum theory of gravity with the same low-energy degrees of freedom as we are considering. Previous results for the corrections to the same potentials, derived historically using Feynman graphs, are verified explicitly, but our approach presents a huge simplification, since starting points for the computations are compact and tedious index contractions and various complicated integral reductions are eliminated from the onset, streamlining the derivations. We also analyze the spin dependence of the results using the KLT factorization, and show how the spinless correction in the framework are easily seen to be independent of the interacting matter considered., Comment: 34 pages, 7 figures, typos corrected, published version

In this paper, we present theoretical details and the underlying architecture of a hybrid optoelectronic correlator that correlates images using Spatial Light Modulators (SLM), detector arrays and Field Programmable Gate Array (FPGA). The proposed architecture bypasses the need for nonlinear materials such as photorefractive polymer films by using detectors instead, and the phase information is yet conserved by the interference of plane waves with the images. However, the output of such a Hybrid Opto-electronic Correlator (HOC) has four terms: two convolution signals and two cross-correlation signals. By implementing a phase stabilization and scanning circuit, the convolution terms can be eliminated, so that the behavior of an HOC becomes essentially identical to that of a conventional holographic correlator (CHC). To achieve the ultimate speed of such a correlator, we also propose an opto-electronic chip which would perform all the electrical processes in a parallel manner. The HOC architecture along with the phase stabilization technique would thus be as good as a CHC, capable of high speed image recognition in a translation invariant manner.

This is a pedagogical introduction to the treatment of quantum general relativity as an effective field theory. It starts with an overview of the methods of effective field theory and includes an explicit example. Quantum general relativity matches this framework and I discuss gravitational examples as well as the limits of the effective field theory. I also discuss the insights from effective field theory on the gravitational effects on running couplings in the perturbative regime., Comment: Presented at the Sixth International School on Field Theory and Gravitation, Petropolis, Brazil, April 2012, to be published in the proceedings. 22 pages, 3 figures

We consider the phenomenology of a dimension-four operator that violates electromagnetic gauge invariance. Its magnitude is severely constrained by the lack of scattering of very low energy electromagnetic radiation off of the Cosmic Microwave Background (CMB) and by the lack of an induced mass when photons propagate in the CMB. We also discuss possible Lorentz-violating extensions of the operator basis. If a bare Proca mass exists and dominates over the induced mass, there is also a tight constraint from high energy scattering., Comment: 9 pages, 1 figure, latexing problem with figure fixed, acknowledgments added

In effective field theories it is common to identify the onset of new physics with the violation of tree-level unitarity. However, we show that this is parametrically incorrect in the case of chiral perturbation theory, and is probably theoretically incorrect in general. In the chiral theory, we explore perturbative unitarity violation as a function of the number of colors and the number of flavors, holding the scale of the "new physics" (i.e. QCD) fixed. This demonstrates that the onset of new physics is parametrically uncorrelated with tree-unitarity violation. When the latter scale is lower than that of new physics, the effective theory must heal its unitarity violation itself, which is expected because the field theory satisfies the requirements of unitarity. In the chiral theory, the self-healing results in a resonant structure with scalar quantum numbers. In the electroweak variant of this argument, the structure must have the properties of the Higgs and must couple proportional to the mass in both gauge boson and fermion scattering. A similar example can be seen in the case of general relativity coupled to multiple matter fields, where iteration of the vacuum polarization diagram restores unitarity. We present arguments that suggest the correct identification should be connected to the onset of inelasticity rather than unitarity violation. We describe how the onset of inelasticity can occur in the effective theory, although it does not appear possible to predict the onset reliably., Comment: 11 pages, 5 figures, typos corrected, reference added