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Riello: EPRL radiative corrections only logarithmic in cosmo constant 
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#1
Feb713, 08:55 PM

Astronomy
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PF Gold
P: 23,101

http://arxiv.org/abs/1302.1781
Spinfoam transition amplitudes only depend lightly on cosmological constant. This is looking good (especially in view of the Hamber Toriumi paper that just appeared.) ==quote Aldo Riello's new paper, page 4== The ERPLFK model can also be extended to the case of General Relativity with cosmological constant in a nontrivial way, both in its Euclidean [25, 26, 27] and Lorentzian [28, 27] versions. Such an extension uses the qdeformed Lorentz group, with the qdeformation parameter related to the cosmological constant, and turns out to be (perturbatively) finite. The existence of a finite model does not mean that the issue of large radiative corrections can be ignored: it may still happen that some higher order graphs have large amplitudes and therefore drive a renormalization flow, possibly even through phase transitions. Qualitatively, the scale which imposes the infrared^{8} finiteness of the theory is given by the cosmological constant, which is of the order of the radius of the Universe; therefore, at our  or smaller  length scales, it can be considered as infinite for practical purposes (but see comments in the conclusions). In this paper, in order to study the simplest EPRLFK divergence, we introduce a cutoff Λ to the SU (2) representations j . The physical meaning of such a cutoff is that of imposing a maximal value for the area operator, which can be thought as the introduction of a finite size for the Universe itself. A bound to the area operator is typical of the qdeformed version of the EPRLFK model. Therefore the introduction of such a cutoff can be hoped to be a simple implementation of the main feature of the qdeformed EPRLFK model within the much more manageable nondeformed version. At the light of this (qualitative) correspondence, the cal culation of this paper can be also given a more physical, though possibly naive, interpretation in which the cutoff Λ is a physical quantity and corresponds  at least in order of magnitude  to the cosmological constant Λ_{CC} expressed in Planck units of area: Λ ≈ Λ_{CC}/l _{P}^{2} ∼ 10^{120} . The goal of this work is to calculate the most divergent contribution to the selfenergy of the EPRLFK spin foam model... Footnote 8: Here, the term “infrared” must be understood as relating to large physical distances; analogously, an “ultraviolet” cutoff, in the sense of a short distance cutoff, is naturally present in any spin foam models, via the existence of the area gap [29]. It must however be kept in mind, that the roles of the words “infrared” and “ultraviolet” are interchanged 


#2
Feb813, 07:14 AM

P: 247

Is this paper in favour of the Hamber Toriumi result ?



#3
Feb813, 08:17 AM

Astronomy
Sci Advisor
PF Gold
P: 23,101

Hi John!
I didn't yet get around to posting the abstract of Aldo Riello's paper. I'll do that now. The reason I mentioned the Hamber Toriumi paper in post #1 in this thread has to do with the fact that a running cosmological constant could turn out to be a liability for a major rival theory (namely Asym Safe QG) if the Hamber Toriumi result holds. This would presumably NOT pose any inconvenience for LQG, because it does NOT involve Lambda running in any essential way. Riello's paper tentatively suggests that in LQG the dependence on Lambda is comparatively weak (logarithmic). The paper focuses on a salient case and makes approximations (which are explained in one of the sections). More work could certainly be done along these same lines! Here's the abstract: http://arxiv.org/abs/1302.1781 SelfEnergy in the Lorentzian ERPLFK Spin Foam Model of Quantum Gravity Aldo Riello (Submitted on 7 Feb 2013) We calculate the most divergent contribution to the selfenergy (or "melonic") graph in the context of the Lorentzian EPRLFK Spin Foam model of Quantum Gravity. We find that such a contribution is logarithmically divergent in the cutoff 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 noncommutativity of the EPRLFK Ymap with the projector onto SL(2,C)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. 55 pages, 8 figures 


#4
Feb913, 10:05 AM

PF Gold
P: 1,957

Riello: EPRL radiative corrections only logarithmic in cosmo constant



#5
Feb1513, 09:45 AM

Astronomy
Sci Advisor
PF Gold
P: 23,101

In his ILQGS talk this week, Haggard cited Riello's paper (slide #33, conclusions) in a way that puts it in larger context and notes the paper's significance.
The ILQGS talk set out 3 main questions at the beginning
==quote slide #33== Gravitational divergences Loop gravity continues to indicate physical cutoffs at the Planck scale: Robust volume gap due to: chaos & low density of states at low volume Meanwhile, Riello is finding divergences at large j (large distance) are tamer than first indicated, only logarithmic: grqc/1302.1781 Loop gravity has a coherent and, so far, consistent view of gravitational divergences. ==endquote== http://relativity.phys.lsu.edu/ilqgs/haggard021213.pdf 


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