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arXiv · 2512.23539

Semiclassical Canovaccio for Composite Operators

Oleg Antipin·Jahmall Bersini·Jacob Hafjall·Giulia Muco·Francesco Sannino
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Abstract

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 $\phi^4$ theory near four dimensions and $\phi^6$ near three dimensions, semiclassically determining the full spectrum of neutral operators in the traceless symmetric Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.

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Oleg Antipin, Jahmall Bersini, Jacob Hafjall, Giulia Muco, Francesco Sannino. 2025-12-29. Semiclassical Canovaccio for Composite Operators. https://arxiv.org/abs/2512.23539

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