EPRL/FK Group Field Theory
Joseph Ben Geloun, Razvan Gurau, Vincent Rivasseau
TL;DR
The note develops a group-space formulation of EPRL/FK spin foam models within Group Field Theory by deriving a propagator as a composition of gauge and simplicity projections. It provides explicit kernels for the simplicity projector $S$ and the propagator $C$, and derives compact expressions for the GFT Feynman amplitudes with a clear face/strand decomposition. It analyzes leading divergences and presents a locality-based subtraction scheme, supported by a saddle-point power-counting analysis that yields precise divergence degrees for representative graphs. The results illuminate the connection to BF theory and Barrett–Crane limits and set the stage for a renormalization program, including possible flow of the Immirzi parameter.
Abstract
The purpose of this short note is to clarify the Group Field Theory vertex and propagators corresponding to the EPRL/FK spin foam models and to detail the subtraction of leading divergences of the model.