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A measure on the space of CFTs and pure 3D gravity
by Alexandre Belin, Alexander Maloney, Florian Seefeld
Submission summary
| Authors (as registered SciPost users): | Florian Seefeld |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2509.04554v2 (pdf) |
| Date submitted: | Jan. 5, 2026, 2:11 p.m. |
| Submitted by: | Florian Seefeld |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We define a normalizable measure on the space of two-dimensional conformal field theories, which we interpret as a maximum ignorance ensemble. We test whether pure quantum gravity in AdS$_3$ is dual to the average over this ensemble. We find a negative answer, which implies that CFTs with a primary gap of order the central charge are highly atypical in our ensemble. We provide evidence that more generally, holographic CFTs are atypical in the space of all CFTs by finding similar results for permutation orbifolds: subgroups of $S_N$ with a good large $N$ limit are very sparse in the space of all subgroups. Along the way, we derive several new results on the space of CFTs. Notably we derive an upper bound on the spacing in central charge between CFTs, which is doubly exponentially small in the large central charge limit.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Florian Seefeld on 2026-01-08 [id 6216]
Dear referees,
Please note that there is a typo in equation 1.5 of the preprint. The right parenthesis inside the integration is supposed to be part of the subscript, so the correct tex code for this equation is
\[
\overline{ \cdot}\equiv \int_{C(c_0,\epsilon_c)} d\mu \cdot \, ,
\]
Best,
the authors