Snyder-de Sitter meets the Grosse-Wulkenhaar model

TL;DR

This paper investigates a scalar field theory on Snyder-de Sitter space, revealing its connection to the Grosse-Wulkenhaar model and identifying a fixed point in its renormalization group flow.

Contribution

It demonstrates that the scalar field theory on Snyder-de Sitter space reduces to a Grosse-Wulkenhaar-like model in certain limits and finds a fixed point in the renormalization group flow.

Findings

The theory in the small curvature and noncommutativity limit resembles the Grosse-Wulkenhaar model.

A fixed point exists in the renormalization group flow of the harmonic and mass terms.

Renormalization behavior differs from the commutative case due to noncommutativity and curvature.

Abstract

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.