# A Multitrace Matrix Model from Fuzzy Scalar Field Theory

@article{OConnor2007AMM, title={A Multitrace Matrix Model from Fuzzy Scalar Field Theory}, author={Denjoe O’Connor and Christian Saemann}, journal={arXiv: High Energy Physics - Theory}, year={2007} }

We present the analytical approach to scalar field theory on the fuzzy sphere which has been developed in arXiv:0706.2493 [hep-th]. This approach is based on considering a perturbative expansion of the kinetic term in the partition function. After truncating this expansion at second order, one arrives at a multitrace matrix model, which allows for an application of the saddle-point method. The results are in agreement with the numerical findings in the literature.

## 8 Citations

### The Multitrace Matrix Model of Scalar Field Theory on Fuzzy CP^n

- Computer Science
- 2010

A high-temperature expansion of scalar quantum field theory on fuzzy CP^n to third order in the inverse temperature is performed using group theoretical methods and this result is rewritten as a multitrace matrix model.

### The phase diagram of scalar field theory on the fuzzy disc

- Physics
- 2015

A bstractUsing a recently developed bootstrapping method, we compute the phase diagram of scalar field theory on the fuzzy disc with quartic even potential. We find three distinct phases with second…

### Triple point of a scalar field theory on a fuzzy sphere

- PhysicsJournal of High Energy Physics
- 2018

A bstractThe model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the…

### Simulation of a scalar field on a fuzzy sphere

- Physics
- 2009

The ϕ4 real scalar field theory on a fuzzy sphere is studied numerically. We refine the phase diagram for this model where three distinct phases are known to exist: a uniformly ordered phase, a…

### A Chern-Simons theory view of noncommutative scalar field theory

- Mathematics
- 2018

We show that a version of Abelian gauge theory on $\mathbb{R}^3_\lambda $, when restricted to a single fuzzy sphere, reduces in the large $N$ limit to the Langmann-Szabo-Zarembo (LSZ) matrix model,…

### Complex (super)-matrix models with external sources and q-ensembles of Chern–Simons and ABJ(M) type

- Computer ScienceJournal of Physics A: Mathematical and Theoretical
- 2020

It is proved that the LSZ matrix model computes the probability of atypically large fluctuations in the Stieltjes–Wigert matrix model, which is a q-ensemble describing U(N) Chern–Simons theory on the three-sphere.

### Triple point of a scalar field theory on a fuzzy sphere

- PhysicsJournal of High Energy Physics
- 2018

The model of a scalar field with quartic self-interaction on the fuzzy sphere has three known phases: a uniformly ordered phase, a disordered phase and a non-uniformly ordered phase, the last of…

### Fuzzy scalar field theory as matrix quantum mechanics

- Physics
- 2011

We study the phase diagram of scalar field theory on a three dimensional Euclidean spacetime whose spatial component is a fuzzy sphere. The corresponding model is an ordinary one-dimensional matrix…

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