Scholarlink

<p>A Hermitian <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\Phi ^4\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi mathvariant="normal">Φ</mi> <mn>4</mn> </msup> </math></EquationSource> </InlineEquation> 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 <i>N</i>-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 <i>N</i>-body harmonic oscillator can also be reformulated in terms of connected correlation functions. The <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(U(1)^N\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>U</mi> <msup> <mrow> <mo stretchy="false">(</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> <mi>N</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>-symmetry allows us to derive loop equations.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Relationship between a \(\Phi ^4\) matrix model and harmonic oscillator systems

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年2月17日

查看全文
  • Harald Grosse,
  • Naoyuki Kanomata,
  • Akifumi Sako,
  • Raimar Wulkenhaar

摘要

A Hermitian \(\Phi ^4\) 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 \(U(1)^N\) U ( 1 ) N -symmetry allows us to derive loop equations.