Asymptotic freedom for $$\lambda \phi ^4_{\star }$$ QFT in Snyder–de Sitter space
S. A. Franchino-Viñas, S. Mignemi
Abstract
Abstract We analyze the model of a self-interacting $$\phi ^4_{\star }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>ϕ</mml:mi><mml:mo>⋆</mml:mo><mml:mn>4</mml:mn></mml:msubsup></mml:math> 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.