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PreprintCC BY 4.0arXiv

Bootstrapping Fermionic Veneziano Amplitudes from Regge Zeros

  • Pongwit Srisangyingcharoen
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Abstract

We extend the Regge-zero bootstrap of the Veneziano amplitude to tree-level scattering with external fermions. We consider the colour-ordered four-point amplitude of a massless scalar and a massless spin-1/2 fermion, in which fermionic resonances appear in the s-channel and bosonic resonances in the t-channel. Factoring out a spinor structure that carries the little-group weight of the amplitude, we bootstrap the resulting reduced amplitude, whose residues in each channel vanish at Regge zeros controlled by the trajectory of the opposite channel. Assuming ultrasoft Regge behaviour and that the residues have no zeros other than Regge zeros, we show that both Regge trajectories are linear and that the maximal spins grow with the level as JF=n+1/2 and JB=m+1. Duality between the fermionic- and bosonic-pole expansions then fixes the reduced amplitude to a Beta function, up to its normalisation and the ratio of the two Regge slopes. Requiring the fermionic and bosonic spectra to be degenerate equates the slopes, and the resulting amplitude coincides with the open superstring amplitude.

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Cite

BibTeXRIS
BibTeX
@misc{srisangyingcharoen2026bootstrapping,
  title = {{Bootstrapping Fermionic Veneziano Amplitudes from Regge Zeros}},
  author = {Pongwit Srisangyingcharoen},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.24754},
  eprint = {2610.24754},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.24754},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Bootstrapping Fermionic Veneziano Amplitudes from Regge Zeros
AU  - Pongwit Srisangyingcharoen
PY  - 2026
DA  - 2026/10/17
PB  - arXiv
DO  - 10.48550/arxiv.2610.24754
UR  - https://arxiv.org/abs/2610.24754
AB  - We extend the Regge-zero bootstrap of the Veneziano amplitude to tree-level scattering with external fermions. We consider the colour-ordered four-point amplitude of a massless scalar and a massless spin-1/2 fermion, in which fermionic resonances appear in the s-channel and bosonic resonances in the t-channel. Factoring out a spinor structure that carries the little-group weight of the amplitude, we bootstrap the resulting reduced amplitude, whose residues in each channel vanish at Regge zeros controlled by the trajectory of the opposite channel. Assuming ultrasoft Regge behaviour and that the residues have no zeros other than Regge zeros, we show that both Regge trajectories are linear and that the maximal spins grow with the level as J_F=n+1/2 and J_B=m+1. Duality between the fermionic- and bosonic-pole expansions then fixes the reduced amplitude to a Beta function, up to its normalisation and the ratio of the two Regge slopes. Requiring the fermionic and bosonic spectra to be degenerate equates the slopes, and the resulting amplitude coincides with the open superstring amplitude.
ER  -