arXiv subjects

Tim R. Morris

Publications and source records attributed to Tim R. Morris.

At least 37 records · Page 2Linked to original sources

arXiv2018

Perturbatively renormalizable quantum gravity

The Wilsonian renormalization group (RG) requires Euclidean signature. The conformal factor of the metric then has a wrong-sign kinetic term, which has a profound effect on its RG properties. In particular around the Gaussian fixed point, it supports a Hilbert space of renormalizable interactions involving arbitrarily high powers of the gravitational fluctuations. These interactions are characterised by being exponentially suppressed for large field amplitude, perturbative in Newton's constant but non-perturbative in Planck's constant. By taking a limit to the boundary of the Hilbert space, diffeomorphism invariance is recovered whilst retaining renormalizability. Thus the so-called conformal factor instability points the way to constructing a perturbatively renormalizable theory of quantum gravity.

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arXiv2017

Conformal anomaly from gauge fields without gauge fixing

We show how the Weyl anomaly generated by gauge fields, can be computed from manifestly gauge invariant and diffeomorphism invariant exact renormalization group equations, without having to fix the gauge at any stage. Regularisation is provided by covariant higher derivatives and by embedding the Maxwell field into a spontaneously broken $U(1|1)$ supergauge theory. We first provide a realisation that leaves behind two versions of the original $U(1)$ gauge field, and then construct a manifestly $U(1|1)$ supergauge invariant flow equation which leaves behind only the original Maxwell field in the spontaneously broken regime.

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arXiv2017

Asymptotic solutions in asymptotic safety

We explain how to find the asymptotic form of fixed point solutions in functional truncations, in particular $f(R)$ approximations. We find that quantum fluctuations do not decouple at large $R$, typically leading to elaborate asymptotic solutions containing several free parameters. By a counting argument, these can be used to map out the dimension of the fixed point solution spaces. They are also necessary to validate the numerical solution, and provide the physical part in the limit that the cutoff is removed: the fixed point equation of state. As an example we apply the techniques to a recent $f(R)$ approximation by Demmel et al, finding asymptotic matches to their numerical solution. Depending on the value of the endomorphism parameter, we find many other asymptotic solutions and fixed point solution spaces of differing dimensions, yielding several alternative scenarios for the equation of state. Asymptotic studies of other $f(R)$ approximations are needed to clarify the picture.

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arXiv2016

Large curvature and background scale independence in single-metric approximations to asymptotic safety

In single-metric approximations to the exact renormalization group (RG) for quantum gravity, it has been not been clear how to treat the large curvature domain beyond the point where the effective cutoff scale $k$ is less than the lowest eigenvalue of the appropriate modified Laplacian. We explain why this puzzle arises from background dependence, resulting in Wilsonian RG concepts being inapplicable. We show that when properly formulated over an ensemble of backgrounds, the Wilsonian RG can be restored. This in turn implies that solutions should be smooth and well defined no matter how large the curvature is taken. Even for the standard single-metric type approximation schemes, this construction can be rigorously derived by imposing a modified Ward identity (mWI) corresponding to rescaling the background metric by a constant factor. However compatibility in this approximation requires the space-time dimension to be six. Solving the mWI and flow equation simultaneously, new variables are then derived that are independent of overall background scale.

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arXiv2016

Fixed point structure of the conformal factor field in quantum gravity

The $\mathcal{O}(\partial^2)$ background independent flow equations for conformally reduced gravity are shown to be equivalent to flow equations naturally adapted to scalar field theory with a wrong sign kinetic term. This sign change is shown to have a profound effect on the renormalization group properties, broadly resulting in a continuum of fixed points supporting both a discrete and a continuous eigenoperator spectrum, the latter always including relevant directions. The properties at the Gaussian fixed point are understood in particular depth, but also detailed studies of the local potential approximation, and the full $\mathcal{O}(\partial^2)$ approximation are given. These results are related to evidence for asymptotic safety found by other authors.

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arXiv2016

The fate of non-polynomial interactions in scalar field theory

We present an exact RG (renormalization group) analysis of $O(N)$-invariant scalar field theory about the Gaussian fixed point. We prove a series of statements that taken together show that the non-polynomial eigen-perturbations found in the LPA (local potential approximation) at the linearised level, do not lead to new interactions, \textit{i.e.} enlarge the universality class, neither in the LPA or treated exactly. Non-perturbatively, their RG flow does not emanate from the fixed point. For the equivalent Wilsonian effective action they can be re-expressed in terms of the usual couplings to polynomial interactions, which can furthermore be tuned to be as small as desired for all finite RG time. For the infrared cutoff Legendre effective action, this can also be done for the infrared evolution. We explain why this is nevertheless consistent with the fact that the large field behaviour is fixed by these perturbations.

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arXiv2016

Manifestly diffeomorphism invariant classical Exact Renormalization Group

We construct a manifestly diffeomorphism invariant Wilsonian (Exact) Renormalization Group for classical gravity, and begin the construction for quantum gravity. We demonstrate that the effective action can be computed without gauge fixing the diffeomorphism invariance, and also without introducing a background space-time. We compute classical contributions both within a background-independent framework and by perturbing around a fixed background, and verify that the results are equivalent. We derive the exact Ward identities for actions and kernels and verify consistency. We formulate two forms of the flow equation corresponding to the two choices of classical fixed-point: the Gaussian fixed point, and the scale invariant interacting fixed point using curvature-squared terms. We suggest how this programme may completed to a fully quantum construction.

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arXiv2016

Background independence in a background dependent renormalization group

Within the derivative expansion of conformally reduced gravity, the modified split Ward identities are shown to be compatible with the flow equations if and only if either the anomalous dimension vanishes or the cutoff profile is chosen to be power law. No solutions exist if the Ward identities are incompatible. In the compatible case, a clear reason is found for why Ward identities can still forbid the existence of fixed points; however, for any cutoff profile, a background independent (and parametrisation independent) flow equation is uncovered. Finally, expanding in vertices, the combined equations are shown generically to become either over-constrained or highly redundant beyond the six-point level.

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arXiv2016

Translational Symmetry Breaking in Higgs & Gauge Theory, and the Cosmological Constant

We argue, at a very basic effective field theory level, that higher dimension operators in scalar theories that break symmetries at scales close to their ultraviolet completion cutoff, include terms that favour the breaking of translation (Lorentz) invariance, potentially resulting in striped, chequered board or general crystal-like phases. Such descriptions can be thought of as the effective low energy description of QCD-like gauge theories near their strong coupling scale where terms involving higher dimension operators are generated. Our low energy theory consists of scalar fields describing operators such as $\bar{q} q$ and $\bar{q} F^{(2n)} q$. Such scalars can have kinetic mixing terms that generate effective momentum dependent contributions to the mass matrix. We show that these can destabilize the translationally invariant vacuum. It is possible that in some real gauge theory such operators could become sufficiently dominant to realize such phases and it would be interesting to look for them in lattice simulations. We present a holographic model of the same phenomena which includes RG running. A key phenomenological motive to look at such states is recent work that shows that the non-linear response in $R^2$ gravity to such short range fluctuations can mimic a cosmological constant. Intriguingly in a cosmology with such a Starobinsky inflation term, to generate the observed value of the present day acceleration would require stripes at the electroweak scale. Unfortunately, low energy phenomenological constraints on Lorentz violation in the electron-photon system appear to strongly rule out any such possibility outside of a disconnected dark sector.

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arXiv2015

Solutions to the reconstruction problem in asymptotic safety

Starting from a full renormalised trajectory for the effective average action (a.k.a. infrared cutoff Legendre effective action) $Γ_k$, we explicitly reconstruct corresponding bare actions, formulated in one of two ways. The first step is to construct the corresponding Wilsonian effective action $S^k$ through a tree-level expansion in terms of the vertices provided by $Γ_k$. It forms a perfect bare action giving the same renormalised trajectory. A bare action with some ultraviolet cutoff scale $Λ$ and infrared cutoff $k$ necessarily produces an effective average action $Γ^Λ_k$ that depends on both cutoffs, but if the already computed $S^Λ$ is used, we show how $Γ^Λ_k$ can also be computed from $Γ_k$ by a tree-level expansion, and that $Γ^Λ_k\toΓ_k$ as $Λ\to\infty$. Along the way we show that Legendre effective actions with different UV cutoff profiles, but which correspond to the same Wilsonian effective action, are related through tree-level expansions. All these expansions follow from Legendre transform relationships that can be derived from the original one between $Γ^Λ_k$ and $S^k$.

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arXiv2015

Background independent exact renormalization group for conformally reduced gravity

Within the conformally reduced gravity model, where the metric is parametrised by a function $f(ϕ)$ of the conformal factor $ϕ$, we keep dependence on both the background and fluctuation fields, to local potential approximation and $\mathcal{O}(\partial^2)$ respectively, making no other approximation. Explicit appearances of the background metric are then dictated by realising a remnant diffeomorphism invariance. The standard non-perturbative Renormalization Group (RG) scale $k$ is inherently background dependent, which we show in general forbids the existence of RG fixed points with respect to $k$. By utilising transformations that follow from combining the flow equations with the modified split Ward identity, we uncover a unique background independent notion of RG scale, $\hat k$. The corresponding RG flow equations are then not only explicitly background independent along the entire RG flow but also explicitly independent of the form of $f$. In general $f(ϕ)$ is forced to be scale dependent and needs to be renormalised, but if this is avoided then $k$-fixed points are allowed and furthermore they coincide with $\hat k$-fixed points.

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arXiv2014

Cosmological back-reaction in modified gravity and its implications for dark energy

We study the effective stress-energy tensor induced by cosmological inhomogeneity in $f(R)=R+cR^2$ and equivalent scalar-tensor theories, motivated both by models of early universe inflation and by phenomenological alternative cosmologies to the standard $Λ$-CDM. We use Green and Wald's framework for averaging over classical fluctuations of short-wavelength $λ$. By ensuring that the leading non-linear terms from the fluctuations of the Einstein terms and the corrections both contribute in the formal limit as $λ\to0$, we derive a diffeomorphism invariant effective stress-energy tensor whose trace is non-vanishing and of the right sign to potentially account for the current acceleration of the universe. However a more phenomenologically acceptable dark energy model would be required if this effect were to fully account for the current acceleration.

gr-qc↗

arXiv2014

On the Existence of Low-Mass Dark Matter and its Direct Detection

Dark Matter (DM) is an elusive form of matter which has been postulated to explain astronomical observations through its gravitational effects on stars and galaxies, gravitational lensing of light around these, and through its imprint on the Cosmic Microwave Background (CMB). This indirect evidence implies that DM accounts for as much as 84.5% of all matter in our Universe, yet it has so far evaded all attempts at direct detection, leaving such confirmation and the consequent discovery of its nature as one of the biggest challenges in modern physics. Here we present a novel form of low-mass DM $χ$ that would have been missed by all experiments so far. While its large interaction strength might at first seem unlikely, neither constraints from particle physics nor cosmological/astronomical observations are sufficient to rule out this type of DM, and it motivates our proposal for direct detection by optomechanics technology which should soon be within reach, namely, through the precise position measurement of a levitated mesoscopic particle which will be perturbed by elastic collisions with $χ$ particles. We show that a recently proposed nanoparticle matter-wave interferometer, originally conceived for tests of the quantum superposition principle, is sensitive to these collisions, too.

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arXiv2014

The local potential approximation in the background field formalism

Working within the familiar local potential approximation, and concentrating on the example of a single scalar field in three dimensions, we show that the commonly used approximation method of identifying the total and background fields, leads to pathologies in the resulting fixed point structure and the associated spaces of eigenoperators. We then show how a consistent treatment of the background field through the corresponding modified shift Ward identity, can cure these pathologies, restoring universality of physical quantities with respect to the choice of dependence on the background field, even within the local potential approximation. Along the way we point out similarities to what has been previously found in the f(R) approximation in asymptotic safety for gravity.

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arXiv2013

Redundant operators in the exact renormalisation group and in the f(R) approximation to asymptotic safety

In this paper we review the definition and properties of redundant operators in the exact renormalisation group. We explain why it is important to require them to be eigenoperators and why generically they appear only as a consequence of symmetries of the particular choice of renormalisation group equations. This clarifies when Newton's constant and or the cosmological constant can be considered inessential. We then apply these ideas to the Local Potential Approximation and approximations of a similar spirit such as the f(R) approximation in the asymptotic safety programme in quantum gravity. We show that these approximations can break down if the fixed point does not support a `vacuum' solution in the appropriate domain: all eigenoperators become redundant and the physical space of perturbations collapses to a point. We show that this is the case for the recently discovered lines of fixed points in the f(R) flow equations.

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arXiv2013

Asymptotic safety in the f(R) approximation

In the asymptotic safety programme for quantum gravity, it is important to go beyond polynomial truncations. Three such approximations have been derived where the restriction is only to a general function f(R) of the curvature R>0. We confront these with the requirement that a fixed point solution be smooth and exist for all non-negative R. Singularities induced by cutoff choices force the earlier versions to have no such solutions. However, we show that the most recent version has a number of lines of fixed points, each supporting a continuous spectrum of eigen-perturbations. We uncover and analyse the first five such lines. Sensible fixed point behaviour may be achieved if one consistently incorporates geometry/topology change. As an exploratory example, we analyse the equations analytically continued to R<0, however we now find only partial solutions.We show how these results are always consistent with, and to some extent can be predicted from, a straightforward analysis of the constraints inherent in the equations.

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arXiv2011

Superluminal group velocity through near-maximal neutrino oscillations

Recently it was suggested that the observation of superluminal neutrinos by the OPERA collaboration may be due to group velocity effects resulting from close-to-maximal oscillation between neutrino mass eigenstates, in analogy to known effects in optics. We show that superluminal propagation does occur through this effect for a series of very narrow energy ranges, but this phenomenum cannot explain the OPERA measurement.

hep-ph↗

arXiv2009

S-matrix equivalence restored

The canonical transformation that maps light-cone Yang-Mills theory to a Lagrangian description of the MHV rules is non-local, consequently the two sets of fields do not necessarily generate the same S-matrix. By deriving a new recursion relation for the canonical transformation expansion coefficients, we find a direct map between these coefficients and tree level light-cone diagrams. We use this to show that, at least up to one-loop with dimensionally regularised MHV vertices, the only difference is the omission of the one-loop amplitudes in which all gluons have positive helicity.

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