Does QFT make sense in non-integer dimensions?

Diego Delmastro; Yan-Yan Li; Dikshant Rathore

Does QFT make sense in non-integer dimensions?

High Energy Physics - Theory 2026-07-06 v1

Authors: Diego Delmastro , Yan-Yan Li , Dikshant Rathore

Abstract

We revisit the old problem of analytically continuing QFTs to fractional dimension $d\in\mathbb C$ . We observe that common theories like QCD and QED have branch cuts in the complex $d$ plane. In particular, many operators in their low-energy CFT have OPEs and scaling dimensions that jump as a function of $d$ .

Cite

@article{arxiv.2607.05338,
  title  = {Does QFT make sense in non-integer dimensions?},
  author = {Diego Delmastro and Yan-Yan Li and Dikshant Rathore},
  journal= {arXiv preprint arXiv:2607.05338},
  year   = {2026}
}

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74 pages