The Snyder-de Sitter Scalar $\varphi^4_{\star}$ Quantum Field Theory in D=2

TL;DR

This paper investigates a two-dimensional noncommutative scalar quantum field theory on Snyder-de Sitter space, demonstrating its one-loop renormalizability and analyzing how curvature and noncommutativity influence its quantum behavior.

Contribution

It introduces a renormalizable 2D scalar field model on Snyder-de Sitter space and computes its beta functions, revealing the effects of noncommutative-curved deformations.

Findings

Model is renormalizable at one-loop level

Beta functions computed for the couplings

Noncommutative-curved effects influence the effective action

Abstract

We study the two-dimensional version of a quartic self-interacting quantum scalar field on a curved and noncommutative space (Snyder-de Sitter). We show that the model is renormalizable at the one-loop level and compute the beta functions of the related couplings. The renormalization group flow is then studied numerically, arriving at the conclusion that noncommutative-curved deformations can yield both relevant and irrelevant contributions to the one-loop effective action.