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Snyder-de Sitter meets the Grosse-Wulkenhaar model. (English) Zbl 1445.83009

Finster, Felix (ed.) et al., Progress and visions in quantum theory in view of gravity: bridging foundations of physics and mathematics. Selected talks presented at the seventh international conference, Leipzig, Germany, October 1–5, 2018. Cham: Birkhäuser. 163-170 (2020).
Summary: 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.
For the entire collection see [Zbl 1446.83001].

MSC:

83C45 Quantization of the gravitational field
83C65 Methods of noncommutative geometry in general relativity
81T17 Renormalization group methods applied to problems in quantum field theory
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