A Dispersive Bootstrap for the Virasoro-Shapiro Amplitude
Abstract
We study the closed-string tree-level Virasoro-Shapiro amplitude using the dispersive S-matrix bootstrap. For the ten-dimensional maximally supersymmetric four-point amplitude, we impose analyticity, crossing symmetry, partial-wave unitarity, and Regge boundedness. With the massless graviton pole kept explicitly, the resulting dispersion relations and crossing null constraints give numerical bounds on the leading low-energy coefficients normalized by the gravitational coupling, which agree at our reference truncation with earlier bounds from smeared functionals. We then introduce a Virasoro-inspired ansatz, which becomes a set of nonlinear relations among Wilson coefficients and shrinks the allowed region toward the Virasoro-Shapiro trajectory. Finally, we study a gravity-pole-subtracted setup, where the regular part of the amplitude has a well-defined forward limit. In this stripped problem, on the slice of the leading coefficient that places the first Virasoro-Shapiro resonance at the cutoff, the nonlinear constraints reduce the allowed region to a small island containing the Virasoro-Shapiro point. Imposing the ansatz to all orders, together with spectral assumptions not used in the numerics, we show analytically that positivity selects the Virasoro-Shapiro spectrum.
Related
- The Virasoro Bootstrap: from the c∼1 desert to coupled Potts
- virasoro_blocks: Software for the 2d bootstrap
- Super Liouville theory on the torus: bootstrap and the super Virasoro minimal string
- Shapiro spikes in driven quantum fluids
- Shapiro steps of superfluid Fermi gases in a ring trap across the BCS--BEC crossover
BibTeX
@misc{xu2026dispersive,
title = {{A Dispersive Bootstrap for the Virasoro-Shapiro Amplitude}},
author = {Yongjun Xu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.19283},
eprint = {2606.19283},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.19283},
}
RIS
TY - UNPB
TI - A Dispersive Bootstrap for the Virasoro-Shapiro Amplitude
AU - Yongjun Xu
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2606.19283
UR - https://arxiv.org/abs/2606.19283
AB - We study the closed-string tree-level Virasoro-Shapiro amplitude using the dispersive S-matrix bootstrap. For the ten-dimensional maximally supersymmetric four-point amplitude, we impose analyticity, crossing symmetry, partial-wave unitarity, and Regge boundedness. With the massless graviton pole kept explicitly, the resulting dispersion relations and crossing null constraints give numerical bounds on the leading low-energy coefficients normalized by the gravitational coupling, which agree at our reference truncation with earlier bounds from smeared functionals. We then introduce a Virasoro-inspired ansatz, which becomes a set of nonlinear relations among Wilson coefficients and shrinks the allowed region toward the Virasoro-Shapiro trajectory. Finally, we study a gravity-pole-subtracted setup, where the regular part of the amplitude has a well-defined forward limit. In this stripped problem, on the slice of the leading coefficient that places the first Virasoro-Shapiro resonance at the cutoff, the nonlinear constraints reduce the allowed region to a small island containing the Virasoro-Shapiro point. Imposing the ansatz to all orders, together with spectral assumptions not used in the numerics, we show analytically that positivity selects the Virasoro-Shapiro spectrum.
ER -