TL;DR
This paper investigates the parity properties of the Lorentzian EPRL spinfoam model, revealing its invariance under the Immirzi parameter sign, and highlights parity-related issues in the graviton propagator.
Contribution
It provides numerical analysis of the Lorentzian EPRL model's parity behavior, showing the amplitude's independence from the Immirzi parameter sign and identifying parity-related asymmetries.
Findings
Vertex amplitude independent of Immirzi sign
Relation between parity-related critical points
Graviton propagator not parity-invariant
Abstract
We study the parity behavior of the Lorentzian EPRL spinfoam model. We demonstrate that the vertex amplitude does not depend on the sign of the Immirzi parameter. We present numerical results for the transition amplitude and the graviton propagator in the large-spin 4-simplex approximation. The results suggest a simple relation between the contributions of the two parity-related critical points. Finally, we observe that the graviton propagator is not invariant under parity-odd permutations of equivalent nodes. Thus, the Lorentzian model has the same chirality problem as the Euclidean.
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