Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space

Abstract

We analyze the model of a self-interacting ${\varphi }_{\star }^4$ scalar field theory in Snyder-de Sitter space. After analytically computing the one-loop beta functions {in the small noncommutativity and curvature limit}, we solve numerically the corresponding system of differential equations, showing that in this limit the model possesses at least one regime in which the theory is asymptotically free. Moreover, in a given region of the parameter space we also observe a peculiar running of the parameter associated to the curvature, which changes its sign and therefore can be interpreted as a transition from an IR de-Sitter space to and UV anti-de Sitter one.

arXiv comment14 pages, 3 figures. v2: corrects factors 2 in eq. (7) and (8), and eq. (19) regarding the discussion of $m_{\mathrm{eff}}$ and ${\alpha }_{\mathrm{eff}}$

References in corpus (33)

• Noncommutative Field Theory
• Quantum Field Theory on Noncommutative Spaces
• The quantum structure of spacetime at the Planck scale and quantum fields
• Noncommutative Perturbative Dynamics
• Quantum mechanics on the noncommutative plane and sphere
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• Two phases of the noncommutative quantum mechanics
• Triply Special Relativity
• Trace Anomalies from Quantum Mechanics
• Scalar Field Theory on Non-commutative Snyder Space-Time
• Perturbative S-matrix for massive scalar fields in global de Sitter space
• Renormalization Group and Decoupling in Curved Space: III. The Case of Spontaneous Symmetry Breaking
• Self-dual noncommutative ϕ^4-theory in four dimensions is a non-perturbatively solvable and non-trivial quantum field theory
• Form factors and decoupling of matter fields in four-dimensional gravity
• Asymptotic safety, string theory and the weak gravity conjecture
• On the renormalization group for the interacting massive scalar field theory in curved space
• Stability of de Sitter spacetime against infrared quantum scalar field fluctuations
• Vacuum effective actions and mass-dependent renormalization in curved space
• Doubly special relativity in de Sitter spacetime
• Geometry of the Grosse-Wulkenhaar Model
• The $\kappa$-(A)dS noncommutative spacetime
• Classical dynamics on curved Snyder space
• Quantum field theory in generalised Snyder spaces
• Worldline Formalism in Snyder Spaces
• Do the gravitational corrections to the beta functions of the quartic and Yukawa couplings have an intrinsic physical meaning?
• To the sphere and back again: de Sitter infrared correlators at NTLO in 1/N
• Worldline approach to noncommutative field theory
• UV/IR Mixing in Nonassociative Snyder phi^4 Theory
• Solution of the self-dual ${\Phi }^4$ QFT-model on four-dimensional Moyal space
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• Discrete fuzzy de Sitter cosmology
• Snyder-de Sitter meets the Grosse-Wulkenhaar model
• Quantum groups, non-commutative Lorentzian spacetimes and curved momentum spaces

Cited by in corpus (19)

• Relaxing cosmological tensions with a sign switching cosmological constant
• Rastall gravity extension of the standard $\Lambda$CDM model: theoretical features and observational constraints
• Non-commutative Geometry from Perturbative Quantum Gravity
• Effect of Snyder-de Sitter model on the Black hole thermodynamics in the context of rainbow gravity
• Geometrizing the Klein-Gordon and Dirac equations in Doubly Special Relativity
• Generalizations of Snyder model to curved spaces
• Schwinger Pair Production and the Extended Uncertainty Principle: Can Heuristic Derivations Be Trusted?
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Noncommutative Yang model and its generalizations
• Casimir effect in Snyder Space
• Quantum gravity phenomenology at the dawn of the multi-messenger era -- A review
• Graphene in curved Snyder space
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Doubly special relativity as a non-local quantum field theory
• Momentum gauge fields from curved momentum space through Kaluza-Klein reduction
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space
• Formal developments in curved momentum space: the quantum field theory roadmap
• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature
• Comparing $f(R)$ modified gravity and noncommutative geometry in the context of dark matter and traversable wormholes: a survey