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PreprintCC BY 4.0arXiv

The origin of amplitude chaos and strings

  • Pallab Basu
  • Anurag Sarkar
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Abstract

We analytically study the peak statistics of an amplitude ensemble to identify the local mechanism responsible for peak repulsion. Our analytical approaches show that a smooth, nondegenerate ensemble of sufficiently differentiable amplitudes exhibits quartic nearest-neighbor repulsion, pnn(S)∼ S4, where S is the spacing between adjacent peaks. We verify this prediction numerically for the tree-level highly excited string scattering amplitudes. Interestingly, we find the quartic repulsion to be robust by varying both the underlying ensemble and the amplitude functions, whereas a tunable cusp model shows that weakening differentiability changes the strength of the repulsion. Peak repulsion therefore defines a local universality class that is not unique to string theory and may occur in amplitude ensembles in other theories.

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Cite

BibTeXRIS
BibTeX
@misc{basu2026origin,
  title = {{The origin of amplitude chaos and strings}},
  author = {Pallab Basu and Anurag Sarkar},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13240},
  eprint = {2610.13240},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13240},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The origin of amplitude chaos and strings
AU  - Pallab Basu
AU  - Anurag Sarkar
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13240
UR  - https://arxiv.org/abs/2610.13240
AB  - We analytically study the peak statistics of an amplitude ensemble to identify the local mechanism responsible for peak repulsion. Our analytical approaches show that a smooth, nondegenerate ensemble of sufficiently differentiable amplitudes exhibits quartic nearest-neighbor repulsion, p_nn(S)∼ S^4, where S is the spacing between adjacent peaks. We verify this prediction numerically for the tree-level highly excited string scattering amplitudes. Interestingly, we find the quartic repulsion to be robust by varying both the underlying ensemble and the amplitude functions, whereas a tunable cusp model shows that weakening differentiability changes the strength of the repulsion. Peak repulsion therefore defines a local universality class that is not unique to string theory and may occur in amplitude ensembles in other theories.
ER  -