• Corpus ID: 10210984

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. 
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7 Citations
Background Citations
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7 Citations

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References

SHOWING 1-10 OF 22 REFERENCES

Fuzzy scalar field theory as a multitrace matrix model

An analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalarField.

Matrix Models on the Fuzzy Sphere

It is demonstrated that the UV/IR mixing problems of this theory are localized to the tadpole diagrams and can be removed by an appropiate (fuzzy) normal ordering of the φ4 vertex.

Perturbative dynamics on the fuzzy S 2 and RP 2

Matrix varphi4 models on the fuzzy sphere and their continuum limits

We demonstrate that the UV/IR mixing problems found recently for a scalar 4 theory on the fuzzy sphere are localized to tadpole diagrams and can be overcome by a suitable modification of the action.…

Simulating the scalar field on the fuzzy sphere

The properties of the phi^4 scalar field theory on a fuzzy sphere are studied numerically. The fuzzy sphere is a discretization of the sphere through matrices in which the symmetries of the space are…

A matrix phase for the ϕ4 scalar field on the fuzzy sphere

This work finds and discusses in detail a new phase called a matrix phase because the geometry of the fuzzy sphere, as expressed by the kinetic term, becomes negligible there and highlights a new aspect of UV-IR mixing.

A Non-perturbative approach to non-commutative scalar field theory

Non-commutative euclidean scalar field theory is shown to have an eigenvalue sector which is dominated by a well-defined eigenvalue density, and can be described by a matrix model. This is…

Numerical simulations of a non-commutative theory: The Scalar model on the fuzzy sphere

We address a detailed non-perturbative numerical study of the scalar theory on the fuzzy sphere. We use a novel algorithm which strongly reduces the correlation problems in the matrix update process,…

The Fuzzy sphere

A model of Euclidean spacetime is presented in which at scales less than a certain length kappa the notion of a point does not exist and the algebra which determines the structure of the model is an algebra of matrices.

NEW CRITICAL BEHAVIOR IN d = 0 LARGE-N MATRIX MODELS

The non-perturbative formulation of 2-dimensional quantum gravity in terms of the large-N limit of matrix models is studied to include the effects of higher order curvature terms. This leads to…