Relationship between a $$\Phi ^4$$ matrix model and harmonic oscillator systems
Abstract
A Hermitian $$\Phi ^4$$ matrix model with a Kontsevich-type kinetic term is studied. It was recently discovered that the partition function of this matrix model satisfies the Schrödinger equation of the N-body harmonic oscillator, and that eigenstates of the Virasoro operators can be derived from this partition function. We extend these results and obtain an explicit formula for such eigenstates in terms of the free energy. Furthermore, the Schrödinger equation for the N-body harmonic oscillator can also be reformulated in terms of connected correlation functions. The $$U(1)^N$$ -symmetry allows us to derive loop equations.
Fields of Study & Subjects
Random Matrices and Applications
Black Holes and Theoretical Physics
Nonlinear Waves and Solitons
Publication details
- Journal / source
- Letters in Mathematical Physics
- Volume
- 116
- Issue
- 1
- Publication date
- 17 February 2026
- Language
- EN