Asymptotic freedom for $\lambda \phi^4_{\star}$ QFT in Snyder-de Sitter space
Abstract
We analyze the model of a self-interacting scalar field theory in Snyder-de Sitter space. After analytically computing the one-loop beta functions {in the small noncommutativity and curvature limit}, we solve numerically the corresponding system of differential equations, showing that in this limit the model possesses at least one regime in which the theory is asymptotically free. Moreover, in a given region of the parameter space we also observe a peculiar running of the parameter associated to the curvature, which changes its sign and therefore can be interpreted as a transition from an IR de-Sitter space to and UV anti-de Sitter one.
Cite
@article{arxiv.1911.08921,
title = {Asymptotic freedom for $\lambda \phi^4_{\star}$ QFT in Snyder-de Sitter space},
author = {Sebastián A. Franchino-Viñas and Salvatore Mignemi},
journal= {arXiv preprint arXiv:1911.08921},
year = {2021}
}
Comments
14 pages, 3 figures. v2: corrects factors 2 in eq. (7) and (8), and eq. (19) regarding the discussion of $m_{\rm eff}$ and $\alpha_{\rm eff}$