Real symmetric Φ4-matrix model as Calogero–Moser model

Harald Grosse; Naoyuki Kanomata; Akifumi Sako; Raimar Wulkenhaar

doi:10.1007/s11005-024-01772-5

Real symmetric Φ4-matrix model as Calogero–Moser model

Harald Grosse, Naoyuki Kanomata, Akifumi Sako, Raimar Wulkenhaar

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We study a real symmetric Φ⁴-matrix model whose kinetic term is given by Tr(EΦ²), where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Schrödinger type equation with Calogero–Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.

Original language	English
Article number	25
Journal	Letters in Mathematical Physics
Volume	114
Issue number	1
DOIs	https://doi.org/10.1007/s11005-024-01772-5
Publication status	Published - Feb 2024

Keywords

81R10
81R12
81T32
81T75
Calogero–Moser model
Matrix model
Noncommutative geometry
Virasoro algebra

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10.1007/s11005-024-01772-5

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title = "Real symmetric Φ4-matrix model as Calogero–Moser model",

abstract = "We study a real symmetric Φ4-matrix model whose kinetic term is given by Tr(EΦ2), where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Schr{\"o}dinger type equation with Calogero–Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.",

keywords = "81R10, 81R12, 81T32, 81T75, Calogero–Moser model, Matrix model, Noncommutative geometry, Virasoro algebra",

author = "Harald Grosse and Naoyuki Kanomata and Akifumi Sako and Raimar Wulkenhaar",

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year = "2024",

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doi = "10.1007/s11005-024-01772-5",

language = "English",

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AU - Grosse, Harald

AU - Kanomata, Naoyuki

AU - Sako, Akifumi

AU - Wulkenhaar, Raimar

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/2

Y1 - 2024/2

N2 - We study a real symmetric Φ4-matrix model whose kinetic term is given by Tr(EΦ2), where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Schrödinger type equation with Calogero–Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.

AB - We study a real symmetric Φ4-matrix model whose kinetic term is given by Tr(EΦ2), where E is a positive diagonal matrix without degenerate eigenvalues. We show that the partition function of this matrix model corresponds to a zero-energy solution of a Schrödinger type equation with Calogero–Moser Hamiltonian. A family of differential equations satisfied by the partition function is also obtained from the Virasoro algebra.

KW - 81R10

KW - 81R12

KW - 81T32

KW - 81T75

KW - Calogero–Moser model

KW - Matrix model

KW - Noncommutative geometry

KW - Virasoro algebra

UR - https://www.scopus.com/pages/publications/85187146000

U2 - 10.1007/s11005-024-01772-5

DO - 10.1007/s11005-024-01772-5

M3 - Article

AN - SCOPUS:85187146000

SN - 0377-9017

VL - 114

JO - Letters in Mathematical Physics

JF - Letters in Mathematical Physics

IS - 1

M1 - 25

ER -

Real symmetric Φ4-matrix model as Calogero–Moser model

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Keywords

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