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Renormalization of the noncommutative phi^3 model through the Kontsevich model
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We point out that the noncommutative selfdual phi^3 model can be mapped to the Kontsevich model, for a suitable choice of the eigenvalues in the latter. This allows to apply known results for the Kontsevich model to the quantization of the field theory, in particular the KdV flows and Virasoro constraints. The 2-dimensional case is worked out explicitly. We obtain nonperturbative expressions for the genus expansion of the free energy and some n-point functions. The full renormalization for finite coupling is found, which is determined by the genus 0 sector only. All contributions in a genus expansion of any n-point function are finite after renormalization. A critical coupling is determined beyond which the model is unstable. The model is free of UV/IR diseases.
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Relationship between a $\Phi^4$ matrix model and harmonic oscillator systems
The paper gives a free-energy formula for Virasoro eigenstates and a connected-correlator form of the Schwinger-Dyson equation for the Phi^4 matrix model with Kontsevich-type kinetic term.
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