Cornering the Heterotic String
Abstract
We study tree-level completions of four-dimensional 𝒩=4 Yang--Mills theory coupled to 𝒩=4 supergravity. Six-point factorization and supersymmetry Ward identities, supplemented by a peculiar-parity restriction on scalar contact terms, impose nonlinear relations between the single- and double-trace Wilson coefficients, ak,q and bk,q, of the four-gluon amplitude. The simplest relation, κ2a0,0=0, excludes the single-trace F4 interaction at nonzero gravitational coupling, despite its compatibility with four-point supersymmetry. On this gravitational branch, five double-trace parameters determine all coefficients through a7,q and b8,q, which are reproduced by a common exponential generating form. Both the heterotic string and a family of infinite-spin-tower (IST) amplitudes realize this structure. Combining these relations with dispersion relations and partial-wave positivity in SO(N) color channels yields a narrow numerical band closely bounded by the heterotic and simplest IST amplitudes. A spin-dependent mass gap excludes the IST spectrum and further localizes the region near the heterotic trajectory. An analytic unitarity analysis of the simplest IST gives N≤48 and g2/(κ2 m2)≤4, matching the upper limits of the heterotic amplitude, where m is the mass of the first massive level. Along the heterotic trajectory, the numerical bounds also sharply constrain the gauge-to-gravity coupling ratio at N=48.
Related
- Threshold Corrections in Heterotic String Theory from Conformal Perturbation Theory
- Quantum action for heterotic string field theory with quantum L-infinity structure
- Axionic Quintessence in Heterotic String Theory
- Heterotic moduli, the double extension and the alpha'^2 metric
- A note on conserved worldsheet supercharges in heterotic pure spinor superstring
BibTeX
@misc{chiang2026cornering,
title = {{Cornering the Heterotic String}},
author = {Li-Yuan Chiang and Yu-tin Huang and He-Chen Weng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12318},
eprint = {2610.12318},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12318},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Cornering the Heterotic String
AU - Li-Yuan Chiang
AU - Yu-tin Huang
AU - He-Chen Weng
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12318
UR - https://arxiv.org/abs/2610.12318
AB - We study tree-level completions of four-dimensional 𝒩=4 Yang--Mills theory coupled to 𝒩=4 supergravity. Six-point factorization and supersymmetry Ward identities, supplemented by a peculiar-parity restriction on scalar contact terms, impose nonlinear relations between the single- and double-trace Wilson coefficients, a_k,q and b_k,q, of the four-gluon amplitude. The simplest relation, κ^2a_0,0=0, excludes the single-trace F^4 interaction at nonzero gravitational coupling, despite its compatibility with four-point supersymmetry. On this gravitational branch, five double-trace parameters determine all coefficients through a_7,q and b_8,q, which are reproduced by a common exponential generating form. Both the heterotic string and a family of infinite-spin-tower (IST) amplitudes realize this structure. Combining these relations with dispersion relations and partial-wave positivity in SO(N) color channels yields a narrow numerical band closely bounded by the heterotic and simplest IST amplitudes. A spin-dependent mass gap excludes the IST spectrum and further localizes the region near the heterotic trajectory. An analytic unitarity analysis of the simplest IST gives N≤48 and g^2/(κ^2 m^2)≤4, matching the upper limits of the heterotic amplitude, where m is the mass of the first massive level. Along the heterotic trajectory, the numerical bounds also sharply constrain the gauge-to-gravity coupling ratio at N=48.
ER -