Melonic Radiative Correction in Four-Dimensional Spinfoam Model with Cosmological Constant

TL;DR

This paper demonstrates that introducing a non-zero cosmological constant in four-dimensional spinfoam models removes infrared divergences, with the melonic radiative correction remaining finite and exhibiting specific scaling behavior.

Contribution

It proves the finiteness of melonic radiative corrections in spinfoam models with a non-zero cosmological constant, contrasting with the divergence in the zero case.

Findings

Radiative correction is finite with non-zero cosmological constant.

Infrared divergence disappears in the presence of a cosmological constant.

Scaling behavior analyzed for small cosmological constant.

Abstract

Infrared divergence is a common feature of spinfoam models with a vanishing cosmological constant but is expected to disappear in presence of a non-vanishing cosmological constant. In this paper, we investigate the spinfoam amplitude with cosmological constant introduced in arXiv:2109.00034 on the melon graph, which is known as the melonic radiative correction. The amplitude closely relates to the state-integral model of complex Chern-Simons theory. We prove that the melonic radiative correction is finite in presence of a non-vanishing cosmological constant, in contrast to the infrared divergence of spinfoam models with a vanishing cosmological constant. In addition, we also analyze the scaling behavior of the radiative correction in the limit of small cosmological constant.