Inducing the Einstein action in QCD-like theories

Donoghue, John F.; Menezes, G.

doi:10.1103/physrevd.97.056022

Cited by 23 publications

(34 citation statements)

References 47 publications

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“…As soon as quantum effects in the matrix model are taken into account, the effective metric h ab will unavoidably acquire a kinetic term, and therefore propagate. More specifically, it is well-known that induced gravity terms arise at one loop, upon integrating out fields that couple to the effective metric [17,18,38]. The induced terms include the cosmological constant and Einstein-Hilbert terms.…”

Section: Induced Gravitymentioning

confidence: 99%

The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang–Mills matrix models

Sperling

Steinacker

2019

Nuclear Physics B

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We consider the SO(4, 1)-covariant fuzzy hyperboloid H 4 n as a solution of Yang-Mills matrix models, and study the resulting higher-spin gauge theory. The degrees of freedom can be identified with functions on classical H 4 taking values in a higher-spin algebra associated to so(4, 1), truncated at spin n. We develop a suitable calculus to classify the higher-spin modes, and show that the tangential modes are stable. The metric fluctuations encode one of the spin 2 modes, however they do not propagate in the classical matrix model. Gravity is argued to arise upon taking into account induced gravity terms. This formalism can be applied to the cosmological FLRW space-time solutions of [1], which arise as projections of H 4 n . We establish a one-to-one correspondence between the tangential fluctuations of these spaces.

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Section: Induced Gravitymentioning

confidence: 99%

The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang–Mills matrix models

Sperling

Steinacker

2019

Nuclear Physics B

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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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“…Theories such as quadratic gravity [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] and Lee-Wick theories [20][21][22][23][24][25][26][27][28] have propagators which contain both quadratic and quartic momentum dependence. In addition to the pole at q 2 = 0, this combination will produce a high mass pole, via…”

Section: Introductionmentioning

confidence: 99%

Unitarity, stability, and loops of unstable ghosts

2019

Self Cite

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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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Inducing the Einstein action in QCD-like theories

Cited by 23 publications

References 47 publications

The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang–Mills matrix models

The fuzzy 4-hyperboloid Hn4 and higher-spin in Yang–Mills matrix models

Quasi-conformal models and the early universe

Unitarity, stability, and loops of unstable ghosts

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