Gravity as Large Scale Structure: Families of CFTs and the Higher-Spin Gap
Abstract
We observe an apparently universal behavior in large N conformal field theory (CFT) in d≥ 2 dimensions: the single-trace, higher-spin gap obeys the parametric bound Δgap ≲ (δc)1/d, where δc is the central charge increment between successive theories. The origin of this bound is explained heuristically, using a generalized notion of branes that interpolate between conformal points in theory space. Seeking a more precise framework for this picture leads to the central concept of families of CFTs, which tacitly underlies various features and puzzles of AdS/CFT. We develop a working definition of families, with inspiration from families of L-functions in number theory, and formulate a family-level version of the gap bound. Interpreted holographically for families of AdSd+1 vacua, this bound, when applicable, rules out Planckian scale separation, constrains the size and number of extra dimensions, and explains simple scaling patterns in string/M-theory. It also accounts for why all known large N vector models have a bounded gap.
Related
- Constraining f(R) gravity and evolving dark energy via large-scale structure and phase-space trajectories
- Statistics of large-scale structure from the transition probability of Lagrangian trajectories
- Hereditary Effective Atom Theory for Large-Scale Atomic Structure Prediction
- KiDS-Legacy: The consistency test of the large-scale structure with Bernardeau-Nishimichi-Taruya transform
- Black bounces to traversable wormholes from pure gravity in four and higher dimensions
BibTeX
@misc{perlmutter2026gravity,
title = {{Gravity as Large Scale Structure: Families of CFTs and the Higher-Spin Gap}},
author = {Eric Perlmutter},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.24496},
eprint = {2610.24496},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.24496},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gravity as Large Scale Structure: Families of CFTs and the Higher-Spin Gap
AU - Eric Perlmutter
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.24496
UR - https://arxiv.org/abs/2610.24496
AB - We observe an apparently universal behavior in large N conformal field theory (CFT) in d≥ 2 dimensions: the single-trace, higher-spin gap obeys the parametric bound Δ_gap ≲ (δc)^1/d, where δc is the central charge increment between successive theories. The origin of this bound is explained heuristically, using a generalized notion of branes that interpolate between conformal points in theory space. Seeking a more precise framework for this picture leads to the central concept of families of CFTs, which tacitly underlies various features and puzzles of AdS/CFT. We develop a working definition of families, with inspiration from families of L-functions in number theory, and formulate a family-level version of the gap bound. Interpreted holographically for families of AdS_d+1 vacua, this bound, when applicable, rules out Planckian scale separation, constrains the size and number of extra dimensions, and explains simple scaling patterns in string/M-theory. It also accounts for why all known large N vector models have a bounded gap.
ER -