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Semiclassical spectrum of the Ising CFT

Oleg Antipin1,*, Jahmall Bersini2,†, Jacob Hafjall3,‡, Giulia Muco3,§, and Francesco Sannino3,4,∥

  • 1Rudjer Boskovic Institute, Division of Theoretical Physics, Bijenička 54, 10000 Zagreb, Croatia
  • 2Albert Einstein Center for Fundamental Physics, Bern University, Sidlerstrasse 5, CH-3012 Bern, Switzerland
  • 3Quantum Theory Center (ℏQTC) at IMADA & D-IAS, Southern Denmark University, Campusvej 55, 5230 Odense M, Denmark
  • 4Department of Physics Ettore Pancini, Università di Napoli Federico II, via Cintia, 80126 Napoli, Italy

  • *Contact author: oantipin@irb.hr
  • †Contact author: jahmall.bersini@unibe.ch
  • ‡Contact author: jahaf21@student.sdu.dk
  • §Contact author: giulia@qtc.sdu.dk
  • ∥Contact author: sannino@qtc.sdu.dk
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Phys. Rev. D 114, 065002 – Published 2 September, 2026

DOI: https://doi.org/10.1103/43ck-2h6m

Abstract

We develop a semiclassical framework to determine scaling dimensions of neutral composite operators in scalar conformal field theories. For the critical Ising λϕ4 theory in d=4−ε, we obtain the full spectrum of composite operators built out of n fields transforming according to the various Lorentz representations to next-to-leading order in the double-scaling limit n→∞ and λ→0 with λn fixed. At any given order, the semiclassical expansion resums an infinite number of Feynman diagrams. Combining our results with existing perturbative computations further yields the complete five-loop scaling dimensions in the ε-expansion for the family of ϕn operators. Finally, extrapolating the semiclassical results to three dimensions leads to a competitive alternative to existing methodologies.

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Phys. Rev. D 114, 065002– Published 2 September, 2026
  • Received 18 November 2025
  • Accepted 20 July 2026
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