Uniform order phase and phase diagram of scalar field theory on fuzzy $\mathbb{C}{P}^n$

Abstract

We study the phase structure of the scalar field theory on fuzzy $\mathbb{C}{P}^n$ in the large $N$ limit. Considering the theory as a hermitian matrix model we compute the perturbative expansion of the kinetic term effective action under the assumption of distributions being close to the semicircle. We show that this model admits also a uniform order phase, corresponding to the asymmetric one-cut distribution, and we find the phase boundary. We compute a non-perturbative approximation to the effective action which enables us to identify the disorder and the non-uniform order phases and the phase transition between them. We locate the triple point of the theory and find an agreement with previous numerical studies for the case of the fuzzy sphere.

22 pages, 3 figures, 2 tables; v2 - typos corrected, version published in JHEP

References in corpus (3)

• A translation-invariant renormalizable non-commutative scalar model
• Noncommutative field theories on $R_{\lambda }^3$: Towards UV/IR mixing freedom
• Fuzzy Scalar Field Theory as Matrix Quantum Mechanics

Cited by in corpus (5)

• Detecting scaling in phase transitions on the truncated Heisenberg algebra
• Bootstrapping Fuzzy Scalar Field Theory
• Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model
• Quantum Gravity as a Multitrace Matrix Model
• Phase transitions in a ${\Phi }^4$ matrix model on a curved noncommutative space