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PreprintarXiv licencearXiv

Closing the loop on Φ4 in AdS3

  • Dean Carmi
  • Riccardo Ciccone
  • Shimon Sukholuski
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Abstract

We compute the one-loop correction to the CFT data of all double-trace operators [ϕϕ]n,ℓ for a Φ4 theory in AdS3, for arbitrary values of n, ℓ, and of the scaling dimension Δϕ>1. Working in the spectral representation, the t-channel one-loop bubble diagram is reduced to a product of spectral integrals dressed by the conformal 6j symbol. Both the spectral integrals and the subsequent sums over residues are performed analytically, yielding finite closed-form expressions for the anomalous dimensions in terms of higher hypergeometric functions. We discuss the structure of the results, including their large-spin and high-energy behaviors, and show that the anomalous dimensions are completely monotonic in spin.

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Cite

BibTeXRIS
BibTeX
@misc{carmi2026closing,
  title = {{Closing the loop on $Φ^4$ in AdS$_3$}},
  author = {Dean Carmi and Riccardo Ciccone and Shimon Sukholuski},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.06589},
  eprint = {2606.06589},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.06589},
}
RIS
TY  - UNPB
TI  - Closing the loop on Φ^4 in AdS_3
AU  - Dean Carmi
AU  - Riccardo Ciccone
AU  - Shimon Sukholuski
PY  - 2026
DA  - 2026/10/08
PB  - arXiv
DO  - 10.48550/arxiv.2606.06589
UR  - https://arxiv.org/abs/2606.06589
AB  - We compute the one-loop correction to the CFT data of all double-trace operators [ϕϕ]_n,ℓ for a Φ^4 theory in AdS_3, for arbitrary values of n, ℓ, and of the scaling dimension Δ_ϕ>1. Working in the spectral representation, the t-channel one-loop bubble diagram is reduced to a product of spectral integrals dressed by the conformal 6j symbol. Both the spectral integrals and the subsequent sums over residues are performed analytically, yielding finite closed-form expressions for the anomalous dimensions in terms of higher hypergeometric functions. We discuss the structure of the results, including their large-spin and high-energy behaviors, and show that the anomalous dimensions are completely monotonic in spin.
ER  -