Relationship between a $Φ^4$ matrix model and harmonic oscillator systems
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913939122552832 |
|---|---|
| author | Grosse, Harald Kanomata, Naoyuki Sako, Akifumi Wulkenhaar, Raimar |
| author_facet | Grosse, Harald Kanomata, Naoyuki Sako, Akifumi Wulkenhaar, Raimar |
| contents | A Hermitian $Φ^4$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09454 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relationship between a $Φ^4$ matrix model and harmonic oscillator systems Grosse, Harald Kanomata, Naoyuki Sako, Akifumi Wulkenhaar, Raimar High Energy Physics - Theory Mathematical Physics 81T32, 81R12, 81T75 A Hermitian $Φ^4$ 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. |
| title | Relationship between a $Φ^4$ matrix model and harmonic oscillator systems |
| topic | High Energy Physics - Theory Mathematical Physics 81T32, 81R12, 81T75 |
| url | https://arxiv.org/abs/2507.09454 |