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Maximizing the spectral gap for free bosonic CFTs

  • Hyeongjoe Chu
  • Yuchan Jung
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Abstract

We study the spectral gap Δ1 of Narain CFTs, the smallest scaling dimension of a nonvacuum U(1)cL× U(1)cR primary, as a function on the Narain moduli space. Using the exceptional isomorphisms for SO+(2,2) and SO+(3,3), we prove the sharp bounds Δ1≤ 2/3 at c=2 and Δ1≤ 3/4 at c=3, with equality exactly at the SU(3)1 and SU(4)1 WZW models up to O(c)× O(c), and we describe local maxima of Δ1. For 4≤ c≤ 12, we compare the Narain moduli space with the densest known Euclidean lattices: an arithmetic obstruction excludes five candidates, a computer-assisted classification shows that E8, K12, and BW16 each admit a unique Narain structure up to lattice automorphisms, and a conceptual argument excludes the Leech lattice.

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Cite

BibTeXRIS
BibTeX
@misc{chu2026maximizing,
  title = {{Maximizing the spectral gap for free bosonic CFTs}},
  author = {Hyeongjoe Chu and Yuchan Jung},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.22633},
  eprint = {2610.22633},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.22633},
}
RIS
TY  - UNPB
TI  - Maximizing the spectral gap for free bosonic CFTs
AU  - Hyeongjoe Chu
AU  - Yuchan Jung
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.22633
UR  - https://arxiv.org/abs/2610.22633
AB  - We study the spectral gap Δ_1 of Narain CFTs, the smallest scaling dimension of a nonvacuum U(1)^c_L× U(1)^c_R primary, as a function on the Narain moduli space. Using the exceptional isomorphisms for SO^+(2,2) and SO^+(3,3), we prove the sharp bounds Δ_1≤ 2/3 at c=2 and Δ_1≤ 3/4 at c=3, with equality exactly at the SU(3)_1 and SU(4)_1 WZW models up to O(c)× O(c), and we describe local maxima of Δ_1. For 4≤ c≤ 12, we compare the Narain moduli space with the densest known Euclidean lattices: an arithmetic obstruction excludes five candidates, a computer-assisted classification shows that E_8, K_12, and BW_16 each admit a unique Narain structure up to lattice automorphisms, and a conceptual argument excludes the Leech lattice.
ER  -