Snyder-de Sitter meets the Grosse-Wulkenhaar model

Abstract

We study an interacting $\lambda {\varphi }_{\star }^4$ scalar field defined on Snyder-de Sitter space. Due to the noncommutativity as well as the curvature of this space, the renormalization of the two-point function differs from the commutative case. In particular, we show that the theory in the limit of small curvature and noncommutativity is described by a model similar to the Grosse-Wulkenhaar one. Moreover, very much akin to what happens in the Grosse-Wulkenhaar model, our computation demonstrates that there exists a fixed point in the renormalization group flow of the harmonic and mass terms.

6 pages. v2: typos corrected. v3: corrections in eq. (14); introduction of ${\alpha }_{\mathrm{eff}}$ instead of $m_{\mathrm{eff}}$

References in corpus (3)

• Kappa Snyder deformations of Minkowski spacetime, realizations and Hopf algebra
• Worldline Formalism in Snyder Spaces
• Twist for Snyder space

Cited by in corpus (5)

• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Casimir effect in Snyder Space
• Graphene in curved Snyder space