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Exact renormalization of a noncommutative \phi^3 model in 6 dimensions
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The noncommutative selfdual \phi^3 model in 6 dimensions is quantized and essentially solved, by mapping it to the Kontsevich model. The model is shown to be renormalizable and asymptotically free, and solvable genus by genus. It requires both wavefunction and coupling constant renormalization. The exact (all-order) renormalization of the bare parameters is determined explicitly, which turns out to depend on the genus 0 sector only. The running coupling constant is also computed exactly, which decreases more rapidly than predicted by the one-loop beta function. A phase transition to an unstable phase is found.
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Cited by 2 Pith papers
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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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Noncommutative Gauge Theories and Gravity
The paper reviews gauge-theoretic formulations of gravity in ordinary and noncommutative spaces based on the authors' earlier works.
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