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<p>We present a novel semiclassical framework tailored to determine the scaling dimensions of heavy neutral composite operators in conformal field theories (CFTs) which are inaccessible with other current methodologies. It utilizes the state-operator correspondence to map the desired scaling dimensions to the semiclassical energy spectrum of periodic homogeneous field configurations on a cylinder. As concrete applications, we provide detailed analyses for the <i>ϕ</i><sup>4</sup> theory near four dimensions and <i>ϕ</i><sup>6</sup> near three dimensions, semiclassically determining the full spectrum of neutral operators transforming according to different Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.</p>

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Semiclassical canovaccio for composite operators

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月13日

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  • Oleg Antipin,
  • Jahmall Bersini,
  • Jacob Hafjall,
  • Giulia Muco,
  • Francesco Sannino

摘要

We present a novel semiclassical framework tailored to determine the scaling dimensions of heavy neutral composite operators in conformal field theories (CFTs) which are inaccessible with other current methodologies. It utilizes the state-operator correspondence to map the desired scaling dimensions to the semiclassical energy spectrum of periodic homogeneous field configurations on a cylinder. As concrete applications, we provide detailed analyses for the ϕ4 theory near four dimensions and ϕ6 near three dimensions, semiclassically determining the full spectrum of neutral operators transforming according to different Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.