Numerical computations of next-to-leading order corrections in spinfoam large-$j$ asymptotics

TL;DR

This paper numerically analyzes the next-to-leading order corrections in the large-$j$ asymptotics of Lorentzian EPRL spinfoam amplitudes, revealing their dependence on the Barbero-Immirzi parameter and quantum corrections to the Regge action.

Contribution

It provides the first detailed numerical computation of $O(1/j)$ corrections in Lorentzian EPRL amplitudes with different boundary states and explores their behavior as a function of the Barbero-Immirzi parameter.

Findings

$O(1/j)$ corrections stabilize to finite constants as $ o\infty$.

Quantum corrections to the Regge action are derived from the $O(1/j)$ contributions.

Dependence of corrections on boundary states and the Barbero-Immirzi parameter is characterized.

Abstract

We numerically study the next-to-leading order corrections of the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) 4-simplex amplitude in the large-$j$ expansions. We perform large-$j$ expansions of Lorentzian EPRL 4-simplex amplitudes with two different types of boundary states, the coherent intertwiners and the coherent spin-network, and numerically compute the leading-order and the next-to-leading order $O(1/j)$ contributions of these amplitudes. We also study the dependences of these $O(1/j)$ corrections on the Barbero-Immirzi parameter $\gamma$. We show that they, as functions of $\gamma$, stabilize to finite real constants as $\gamma\to\infty$. Lastly, we obtain the quantum corrections to the Regge action because of the $O(1/j)$ contribution to the spinfoam amplitude.