Constraining the spectral gap of 2d CFTs just above c=1
Abstract
We numerically study the space of compact unitary two-dimensional conformal field theories (2d CFTs) with central charge c>1 using the modular bootstrap. We focus on bounding the spectral gap Δgap of such theories, namely the smallest scaling dimension among the non-vacuum primary operators. We use both a primal method that directly searches for consistent spectra and a dual method that yields rigorous exclusions. A key feature of our analysis is requiring the degeneracies of primary operators to be positive integers. At c very near $1$, the integrality constraint greatly reduces the allowed spectral gap in both methods. For example, at c−1 = 3× 10−3 integrality strengthens the rigorous bound from Δgap ≲ 0.5 to Δgap < 0.041. Our results suggest that the spectral gap might vanish as c approaches $1$ from above.
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BibTeX
@misc{benjamin2026constraining,
title = {{Constraining the spectral gap of 2d CFTs just above c=1}},
author = {Nathan Benjamin and Kevin Langhoff and Wei Li and Jesse Thaler},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07011},
eprint = {2611.07011},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07011},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Constraining the spectral gap of 2d CFTs just above c=1
AU - Nathan Benjamin
AU - Kevin Langhoff
AU - Wei Li
AU - Jesse Thaler
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07011
UR - https://arxiv.org/abs/2611.07011
AB - We numerically study the space of compact unitary two-dimensional conformal field theories (2d CFTs) with central charge c>1 using the modular bootstrap. We focus on bounding the spectral gap Δ_gap of such theories, namely the smallest scaling dimension among the non-vacuum primary operators. We use both a primal method that directly searches for consistent spectra and a dual method that yields rigorous exclusions. A key feature of our analysis is requiring the degeneracies of primary operators to be positive integers. At c very near $1$, the integrality constraint greatly reduces the allowed spectral gap in both methods. For example, at c−1 = 3× 10^−3 integrality strengthens the rigorous bound from Δ_gap ≲ 0.5 to Δ_gap < 0.041. Our results suggest that the spectral gap might vanish as c approaches $1$ from above.
ER -