Gauge assisted quadratic gravity: A framework for UV complete quantum gravity

Donoghue, John F.; Menezes, G.

doi:10.1103/physrevd.97.126005

Cited by 49 publications

(58 citation statements)

References 92 publications

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“…The resonance parameters are then m 2 R = m 2 + iγ. The point here is that the normal resonances and ghost-like resonances have the structure iD(q) ∼ Zi q 2 − m 2 + iZγ (6) with Z = +1 for a normal resonance and Z = −1 for the ghost resonance. The change of the two signs together is important.…”

Section: Ghost Resonancesmentioning

confidence: 98%

Unitarity, stability, and loops of unstable ghosts

2019

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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. * Electronic address: donoghue@physics.umass.edu † Electronic address: gabrielmenezes@ufrrj.br arXiv:1908.02416v2 [hep-th] 21 Aug 2019 1.1. Unitarity with normal resonances Unitarity describes the conservation of probability for the S-matrix. It stateswhere we used the definition of the transfer matrix T , namely S = 1 + iT . Here the associated states are the asymptotic single and multiparticle states of the theory. In processes that involve loop diagrams, the sum over real intermediate states can by accomplished by the Cutkosky cutting rules [30] which project out the on-shell states. Procedurally we often look first at the free field theory to identify the free particles. Then when we include interactions, some of these particles become unstable and no longer appear as the asymptotic states of the theory. As far as the S-matrix is concerned, this is a significant change. The particles were originally needed in the Hilbert space for completeness, but then are no longer present in the interacting theory. The question then arises of how to treat such unstable particles in unitarity relations. Should one include them in the sums over states required for unitarity?The answer was provided by Veltman in 1963 [31], see also [32][33][34][35]. He showed that unitarity is indeed satisfied by the inclusion of only the asymptotically stable states. Cuts are not to be taken through the unstable particles, and unstable particles are not to be included in unitarity sums.However, there is a corollary which is useful in practice. In the narrow-width approximation, where the coupling to the decay products is taken to be very small, the off-resonance production becomes small and only resonance production is important. As we demonstrate in Sec. 6, in this limit a cut taken through the unstable particle with its width set to zero reproduces the same result as a cut through the decay products.This combination reinforces our intuition. The full calculation only requires the stable states, as unitarity demands. But when particles are nearly stable, we may approximate them as being stable in practical calculations. Unstable ghos...

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Section: Ghost Resonancesmentioning

confidence: 98%

Unitarity, stability, and loops of unstable ghosts

2019

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“…Quadratic gravity [10][11][12] is an approach that keeps the curvature squared terms in the fundamental action at all energies. It is a renormalizable [10] and unitary [6] quantum field theory.…”

Section: Pacs Numbersmentioning

confidence: 99%

“…In normal resonances, this leads to the phase of elastic scattering moving counterclockwise through 90 o on the Argand diagram. In quadratic gravity we have calculated the unitary amplitude for scattering in the spin-two channel [12]…”

Section: Pacs Numbersmentioning

confidence: 99%

Arrow of Causality and Quantum Gravity

Donoghue

Menezes

2019

Phys. Rev. Lett.

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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. PACS numbers:When caught making a sign mistake in a phase, a colleague would say: "Physics does not depend on whether we use +i or −i", and happily change the sign. At first sight, this phrase seems true. Classical fields are real. The probabilities of quantum mechanics are absolute values squared. Measurements in physics do not seem to care if we defined √ −1 as +i or −i. On second thought, the sign in front of i often does make a major difference. We define time development byThis results in "positive energy" being defined via e −iEt/ . Canonical quantization is defined viaThe path integral treatment of quantum physics is defined using e iS , not e −iS (in units of = c = 1), with S being the action. The Feynman propagator has very important sign conventions in both the numerator and the denominator, withwith infinitesimal and positive. We see that the specific signs in front of i are important in the formalism of quantum mechanics. On third thought, we can see that these signs are a convention, although they do tie in with another feature of our physical description -in particular the time direction (arrow) of causality.In somewhat colloquial language, we would describe causality as "there is no effect before the cause". In relativistic quantum theories of course, one must be careful about what one means by "before". As a simple example, consider the Feynman diagram shown in Figure 1. The Feynman propagator in coordinate space includes both forward and backward propagation in timeFIG. 1: The simple Feynman diagram on the left is decomposed into two time ordered diagrams. In one of the time orderings the final particles emerge before the initial particles have annihilated.withwith E q = q 2 + m 2 and D back F (x) = (D for F (x)) * . What we commonly refer to as positive frequency, or e −iEt , is propagated forward in time and negative frequency backwards in time. However, we see that in one time ordering the final state particles (the effect) emerge before the initial particles have interacted (the cause). So our colloquial notion of causality is inadequate.We note in passing that the time advance of the final state vertex is not observable -due to the uncertainty principle. The time difference of the vertices is of order ∆t ∼ 1/E, where E is the center of mass energy. The time localization of the initial state ...

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“…The "quasi" of "quasi-conformal" is important. It reminds us that the Einstein-Hilbert term and other Weyl-breaking parameters can be present in the Lagrangian, generated, for example, through dimensional transmutation and various quantum effects [3,6,[15][16][17][18][19][20][21][22][23]. Note that an exactly Weyl invariant model would not be physically different from a Weyl-breaking one; indeed, any exactly conformal model can be written as a non-conformal one by fixing a gauge for Weyl symmetry and, conversely, any model of gravity coupled to an arbitrary matter sector can always be made exactly Weyl invariant 4 .…”

Section: Introductionmentioning

confidence: 98%

Quasi-conformal models and the early universe

Salvio

2019

Eur. Phys. J. C

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Extensions of the Standard Model and general relativity featuring a UV fixed point can leave observable implications at accessible energies. Although mass parameters such as the Planck scale can appear through dimensional transmutation, all fundamental dimension-4 operators can (at least approximately) respect Weyl invariance at finite energy. An example is the Weyl-squared term, whose consistency and observational consequences are studied. This quasi-conformal scenario emerges from the UV complete quadratic gravity and is a possible framework for inflation. We find two realizations. In the first one the inflaton is a fundamental scalar with a quasiconformal non-minimal coupling to the Ricci scalar. In this case the field excursion must not exceed the Planck mass by far. An example discussed in detail is hilltop inflation. In the second realization the inflaton is a pseudo-Goldstone boson (natural inflation). In this case we show how to obtain an elegant UV completion within an asymptotically free QCD-like theory, in which the inflaton is a composite scalar due to new strong dynamics. We also show how efficient reheating can occur. Unlike the natural inflation based on Einstein gravity, the tensor-to-scalar ratio is well below the current bound set by Planck. In both realizations mentioned above, the basic inflationary formulae are computed analytically and, therefore, these possibilities can be used as simple benchmark models.---

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Gauge assisted quadratic gravity: A framework for UV complete quantum gravity

Cited by 49 publications

References 92 publications

Unitarity, stability, and loops of unstable ghosts

Unitarity, stability, and loops of unstable ghosts

Arrow of Causality and Quantum Gravity

Quasi-conformal models and the early universe

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