S. A. Franchino-Viñas, S. Mignemi
Published 2019-12-23Version 1
We study an interacting $\lambda\,\phi^4_{\star}$ 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.
Comments: 6 pages. This is a pre-print of the following chapter: Franchino-Vi\~nas and Mignemi, Snyder-de Sitter meets the Grosse-Wulkenhaar Model, published in Progress and Visions in Quantum Theory in View of Gravity - Bridging Foundations of Physics and Mathematics, edited by Finster, Giulini, Kleiner and Tolksdorf, Birkh\"auser (Trademark), reproduced with permission of Springer Nature Switzerland AG
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