Melonic radiative correction in four-dimensional spinfoam model with a cosmological constant

Infrared divergence is a common feature of spinfoam models with a vanishing cosmological constant but is expected to disappear in presence of a nonvanishing cosmological constant. In this paper, we investigate the spinfoam amplitude with cosmological constant 1 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 nonvanishing 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.