https://doi.org/10.1140/epjc/s10052-020-7918-6
Regular Article - Theoretical Physics
Asymptotic freedom for 
QFT in Snyder–de Sitter space
1
Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, C.C. 67 (1900), La Plata, Argentina
2
Theoretisch-Physikalisches Institut, Friedrich Schiller Universität Jena, Max Wien Platz 1, 07743, Jena, Germany
3
Dipartimento di Matematica e Informatica, Università di Cagliari, viale Merello 92, 09123, Cagliari, Italy
4
INFN, Sezione di Cagliari, Cittadella Universitaria, 09042, Monserrato, Italy
* e-mail: sa.franchino@uni-jena.de
Received:
4
February
2020
Accepted:
9
April
2020
Published online:
8
May
2020
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.
© The Author(s), 2020
