Spin foam propagator: A new perspective to include the cosmological constant

Abstract

In recent years, the calculation of the first non-vanishing order of the metric 2-point function or graviton propagator in a semiclassical limit has evolved as a standard test for the credibility of a proposed spin foam model. The existing results of spinfoam graviton propagator rely heavily on the so-called double scaling limit where spins j are large and the Barbero-Immirzi parameter γ is small such that the area A ∝ jγ is approximately constant. However, it seems that this double scaling limit is bound to break down in models including a cosmological constant. We explore this in detail for the recently proposed model [7] by Haggard, Han, Kaminski and Riello and discuss alternative definitions of a graviton propagator, in which the double scaling limit can be avoided.PACS numbers: 04.60.Pp * Electronic address: zhuang2014@fau.edu 1 See e.g. [17,18,[24][25][26][27] for the recent results on spinfoam graviton propagator and 3-point function. 2 f denotes a triangle in the 4-simplex. Θ f denotes a dihedral angle.

Emergent four-dimensional linearized gravity from a spin foam model

“…In this paper we mainly discuss the convergence of critical solutions under the semiclassical continuum limit. In a companion paper [61], we report the result of graviton propagator and the continuum limit, in which we apply gauge fixings to remove zero modes.…”

Spinfoam on Lefschetz Thimble: Markov Chain Monte-Carlo Computation of Lorentzian Spinfoam Propagator

“…where S is given in (10). Recall that when λj ab ∈ Z/2, λS is defined up to 2πiZ because it contains logarithms which are multi-valued, so e λS is single-valued.…”

“…1 otherwise. 10 As suggested in [44], M should be greater than or equal to n 4. Create x cand s of each chain by…”

“…We choose the Barbero-Immirzi parameter as γ = −0.1 in the above numerics. The λ 3 behavior of the spinfoam propagator can be seen analytically, by the known leading order formula [5,[7][8][9][10]:…”

“…The n-point functions in Loop Quantum Gravity (LQG) [1][2][3][4], which is a promising candidate of the quantum gravity theory, have been introduced in [5,6]. In [7][8][9][10], analysis has been carried out on the 2-point correlation function for the Penrose metric operators in the spinfoam model-the covariant formulation of LQG [2,[11][12][13][14]. This 2-point functions are usually called the spinfoam propagator.…”