Self-Energy of the Lorentzian EPRL-FK Spin Foam Model of Quantum Gravity

TL;DR

This paper computes the leading divergence in the self-energy graph of the Lorentzian EPRL-FK spin foam model, revealing a logarithmic divergence influenced by boundary data and non-commutativity effects, with implications for quantum gravity.

Contribution

It provides the first detailed calculation of the divergence structure in the Lorentzian EPRL-FK model's self-energy graph, highlighting the role of face amplitude choices and boundary data dependence.

Findings

Self-energy contribution is logarithmically divergent.

Boundary data dependence differs from the bare propagator.

Non-commutativity of the Y-map affects the boundary data influence.

Abstract

We calculate the most divergent contribution to the non-degenerate sector of 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 face-splitting 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-map 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.