Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space

Abstract

In this contribution, we summarize our recent studies of the phase structure of the Grosse-Wulkenhaar model and its connection to renormalizability. Its action contains a special term that couples the field to the curvature of the noncommutative background space. We first analyze the numerically obtained phase diagram of the model and its three phases: the ordered, the disordered, and the noncommutative stripe phase. Afterward, we discuss the analytical derivation of the effective action and the ordered-to-stripe transition line, and how the obtained expression successfully explains the curvature-induced shift of the triple point compared to the model without curvature. This shift also causes the removal of the stripe phase and makes the model renormalizable.

arXiv commentCOST Action CA18108: Workshop on theoretical aspects of quantum gravity, 1-3 September 2022, Belgrade

References in corpus (26)

• Quantum Field Theory on Noncommutative Spaces
• Noncommutative Perturbative Dynamics
• Minimal Length Scale Scenarios for Quantum Gravity
• Duality in Scalar Field Theory on Noncommutative Phase Spaces
• Renormalisation of ϕ^4-theory on noncommutative R^2 in the matrix base
• Stripes from (noncommutative) stars
• On some integrals over the U(N) unitary group and their large N limit
• Geometry of the Grosse-Wulkenhaar Model
• Probing the fuzzy sphere regularisation in simulations of the 3d λϕ^4 model
• Asymptotic freedom for $\lambda {\varphi }_{\star }^4$ QFT in Snyder-de Sitter space
• The Continuum Phase Diagram of the 2d Non-Commutative lambda phi**4 Model
• Uniform order phase and phase diagram of scalar field theory on fuzzy $\mathbb{C}{P}^n$
• On the Phase Structure of Commuting Matrix Models
• The Phase Diagram of Scalar Field Theory on the Fuzzy Disc
• The Snyder-de Sitter Scalar ${\phi }_{\star }^4$ Quantum Field Theory in D=2
• Asymmetric hermitian matrix models and fuzzy field theory
• Second moment fuzzy-field-theory-like matrix models
• Triple Point of a Scalar Field Theory on a Fuzzy Sphere
• Spontaneous breaking of translational invariance in non-commutative lambda phi^4 theory in two dimensions
• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• A Multitrace Approach to Noncommutative Φ_2^4
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Renormalization on the fuzzy sphere
• One-loop structure of the U(1) gauge model on the truncated Heisenberg space
• Approximate treatment of noncommutative curvature in quartic matrix model
• Remarks on the eigenvalues distributions of D\leq 4 Yang-Mills matrix models

Cited by in corpus (1)

• Pinpointing Triple Point of Noncommutative Matrix Model with Curvature