Radiative Corrections in the Boulatov-Ooguri Tensor Model: The 2-Point Function

Geloun, Joseph Ben; Bonzom, Valentin

doi:10.1007/s10773-011-0782-2

Cited by 94 publications

(119 citation statements)

References 46 publications

(100 reference statements)

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“…• also η 23 , η 34 , η 14 acquire an iπ; 36 Remark that this gauge fixing is compatible with the previous one, done at the very beginning of this section.…”

Section: Solutions Of Type [Eucl] ([Lor]supporting

confidence: 71%

“…For the moment, we just remark that a possible mechanism for this is the emergency of non-trivial gluing conditions due to the dependence of the renormalized propagator on the spins {j a }. Indeed, something very similar happens in the SU (2)-BF case (see [36]), where the result of the melon renormalization procedure is the introduction of a group Laplacian in the renormalized GFT Lagrangian.…”

Section: Discussionmentioning

confidence: 81%

“…Despite this, it has the merit of being directly generalizable to the EPRL-FK model, while most of the other techniques one can find in the literature make substantial use of the peculiar properties of the particularly favourable BF-theory structure. The interested reader can find a much more thorough analysis of the melon graph in SU (2)-BF theory, and in particular of the subleading terms in its amplitude, in [36]. 24 Explicitly:…”

Section: Parity Related Tetrahedramentioning

confidence: 99%

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Self-energy of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov model of quantum gravity

Riello

2013

Phys. Rev. D

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We calculate the most divergent contribution to non-degenerate sectorof the self-energy (or "melonic") graph in the context of the Lorentzian EPRL-FK Spin Foam model of Quantum Gravity. We find that such a contribution is logarithmically divergent in the cut-off over the SU (2)-representation spins when one chooses the face amplitude guaranteeing the facesplitting invariance of the foam. We also find that the dependence on the boundary data is different from that of the bare propagator. This fact has its origin in the non-commutativity of the EPRL-FK Y γ -map with the projector onto SL(2, )-invariant states. In the course of the paper, we discuss in detail the approximations used during the calculations, its geometrical interpretation as well as the physical consequences of our result.

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“…• also η 23 , η 34 , η 14 acquire an iπ; 36 Remark that this gauge fixing is compatible with the previous one, done at the very beginning of this section.…”

Section: Solutions Of Type [Eucl] ([Lor]supporting

confidence: 71%

Section: Discussionmentioning

confidence: 81%

Section: Parity Related Tetrahedramentioning

confidence: 99%

See 1 more Smart Citation

Self-energy of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov model of quantum gravity

Riello

2013

Phys. Rev. D

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“…We focus on models whose kinetic operator is the Laplace-Beltrami operator on SU(2) 4 , together with a 'mass term'. A motivation for this choice is that the presence of the Laplacian seems to be required by GFT renormalisation [65][66][67][68][69]. The equation (5.21) for the function ξ then becomes (setting the g ′′ I which are arbitrary equal to the identity)…”

Section: Jhep06(2014)013mentioning

confidence: 99%

Homogeneous cosmologies as group field theory condensates

Gielen

Oriti

Sindoni

2014

J. High Energ. Phys.

132

256

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We give a general procedure, in the group field theory (GFT) formalism for quantum gravity, for constructing states that describe macroscopic, spatially homogeneous universes. These states are close to coherent (condensate) states used in the description of Bose-Einstein condensates. The condition on such states to be (approximate) solutions to the quantum equations of motion of GFT is used to extract an effective dynamics for homogeneous cosmologies directly from the underlying quantum theory. The resulting description in general gives nonlinear and nonlocal equations for the 'condensate wavefunction' which are analogous to the Gross-Pitaevskii equation in Bose-Einstein condensates. We show the general form of the effective equations for current quantum gravity models, as well as some concrete examples. We identify conditions under which the dynamics becomes linear, admitting an interpretation as a quantum-cosmological Wheeler-DeWitt equation, and give its semiclassical (WKB) approximation in the case of a kinetic term that includes a Laplace-Beltrami operator. For isotropic states, this approximation reproduces the classical Friedmann equation in vacuum with positive spatial curvature. We show how the formalism can be consistently extended from Riemannian signature to Lorentzian signature models, and discuss the addition of matter fields, obtaining the correct coupling of a massless scalar in the Friedmann equation from the most natural extension of the GFT action. We also outline the procedure for extending our condensate states to include cosmological perturbations. Our results form the basis of a general programme for extracting effective cosmological dynamics directly from a microscopic non-perturbative theory of quantum gravity.

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“…The latter contains Laplace operators, but this is exclusively motivated by field theory: without the Laplace operators no consistent renormalization scheme can be implemented, as was first remarked in [48], in a slightly different but nonetheless very similar context. There is at this stage no satisfying gravitational understanding of such terms, which is the main reason why this SU(2) model was originally not proposed as a 3d quantum gravity model, but only as an interesting toy-model.…”

Section: A One-loop Beta Functionsmentioning

confidence: 99%

Group field theory in dimension4−ϵ

Carrozza

2015

Phys. Rev. D

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Building on an analogy with ordinary scalar field theories, an ε-expansion for rank-3 tensorial group field theories with gauge invariance condition is introduced. This allows to continuously interpolate between the dimension four group SU(2) × U(1) and the dimension three SU(2). In the first situation, there is a unique marginal ϕ 4 coupling constant, but in contrast to ordinary scalar field theory this model is asymptotically free. In the SU(2) case, the presence of two marginally relevant ϕ 6 coupling constants and one ϕ 4 super-renormalizable interaction spoils this interesting property. However, the existence of a non-trivial fixed point is established in dimension 4 − ε, hence suggesting that the SU(2) theory might be asymptotically safe. To pave the way to future non-perturbative calculations, the present perturbative results are discussed in the framework of the effective average action.

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Radiative Corrections in the Boulatov-Ooguri Tensor Model: The 2-Point Function

Cited by 94 publications

References 46 publications

Self-energy of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov model of quantum gravity

Self-energy of the Lorentzian Engle-Pereira-Rovelli-Livine and Freidel-Krasnov model of quantum gravity

Homogeneous cosmologies as group field theory condensates

Group field theory in dimension4−ϵ

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