Learning the open string spectrum with neural networks
Abstract
The tree-level open superstring has an integer mass-squared spectrum on linear Regge trajectories. To what extent is this fixed by consistency conditions: locality, analyticity, crossing, unitarity together with the requirement that 2→2 scattering minimize the entanglement it generates? Using the local two-channel crossing symmetric dispersion relation with one-parameter ambiguity (λ-CSDR) we set up a bootstrap treating both the mass-squared spectrum and the partial-wave coefficients as unknowns which lets the machine learning algorithm to learn the mass-squared spectrum and partial-wave coefficients simultaneously, going beyond earlier work in which the spectrum was fixed. Using the local three-channel crossing symmetric dispersion relation with one-parameter ambiguity we obtain, within the class of amplitudes with soft Regge behavior and infinite higher-spin tower, a bound on the leading Wilson coefficients that we compare with existing bounds and trace to spin-0 dominance. We locate the Virasoro-Shapiro amplitude in the allowed region of the Wilson coefficients space. For amplitudes with two-channel crossing symmetry we find that a Non-dual amplitude exhibits a Polchinski-Strassler type transition from Regge to power-law behavior.
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BibTeX
@misc{chowdhury2026learning,
title = {{Learning the open string spectrum with neural networks}},
author = {Debapriyo Chowdhury},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27667},
eprint = {2610.27667},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27667},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Learning the open string spectrum with neural networks
AU - Debapriyo Chowdhury
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27667
UR - https://arxiv.org/abs/2610.27667
AB - The tree-level open superstring has an integer mass-squared spectrum on linear Regge trajectories. To what extent is this fixed by consistency conditions: locality, analyticity, crossing, unitarity together with the requirement that 2→2 scattering minimize the entanglement it generates? Using the local two-channel crossing symmetric dispersion relation with one-parameter ambiguity (λ-CSDR) we set up a bootstrap treating both the mass-squared spectrum and the partial-wave coefficients as unknowns which lets the machine learning algorithm to learn the mass-squared spectrum and partial-wave coefficients simultaneously, going beyond earlier work in which the spectrum was fixed. Using the local three-channel crossing symmetric dispersion relation with one-parameter ambiguity we obtain, within the class of amplitudes with soft Regge behavior and infinite higher-spin tower, a bound on the leading Wilson coefficients that we compare with existing bounds and trace to spin-0 dominance. We locate the Virasoro-Shapiro amplitude in the allowed region of the Wilson coefficients space. For amplitudes with two-channel crossing symmetry we find that a Non-dual amplitude exhibits a Polchinski-Strassler type transition from Regge to power-law behavior.
ER -