Explain special near-unitary behavior of fractional-dimensional CFTs

Explain why, in conformal field theories defined in non-integer dimensions that become unitary when continued to integer d, low-lying observables often appear unitary with violations arising only from high-dimension evanescent operators, and provide a theoretical framework accounting for this phenomenon.

Background

The thesis reviews that fractional-dimensional CFTs are generically non-unitary due to evanescent operators but remarks on an empirical regularity: theories that are unitary at integer d often appear effectively unitary at low orders away from integer d, with non-unitarity showing up only in high-dimension sectors.

The authors explicitly state that this pattern is not currently understood, indicating a conceptual gap in our understanding of analytically continued CFTs and the role of evanescent operators.

References

We note that there does appear to be something special about the non-unitary CFTs that are unitary when continued to integer d, as opposed to other CFTs. For example, they are seemingly unitary at low orders, with violation only due to the aforementioned high-dimension evanescent operators. This is not understood at present.

— Quantum field theories with many fields  (2603.04481 - Fraser-Taliente, 4 Mar 2026) in Subsection "Justification: continuous dimension  Automatic non-unitarity in fractional dimensions" (Chapter 2, Section 2.6)