Infrared Consistency and the Uniqueness of String Amplitudes
Abstract
Recent work has shown that maximal supersymmetry, combined with a particular scalar-parity condition at six points, imposes nonlinear constraints on four-point effective field theory amplitudes. Numerical bootstrap studies incorporating unitarity provide evidence for the Veneziano amplitude in maximally supersymmetric Yang--Mills theory and for the Virasoro--Shapiro amplitude, together with infinite-spin alternatives, in supergravity. In this paper, we establish these constraints to all orders in the low-energy expansion. The derivation uses a collinear limit in which three three-particle factorization channels, or six in gravity, simultaneously go on shell. A scalar-parity projection and a single discrete R-symmetry eliminate the unknown six-point remainder, leaving three-term master equations determined entirely by four-point factorization. Solving these equations proves the conjectured exponential forms and provides a map that reconstructs the full amplitude from its regular forward limit. Under explicit analytic and positive dispersive assumptions, the fixed reflection-even part of the gauge-theory exponential determines the forward spectral measure and uniquely selects the Veneziano amplitude, with finite-spin residues emerging as a consequence. In gravity, the exponential leaves the forward measure undetermined: a measure supported at a single massive level reconstructs an amplitude with infinitely many exchanged spins at that mass. Finite-spin support at the lowest massive pole is therefore an additional assumption required to select the Virasoro--Shapiro amplitude within the stated ultraviolet framework.
Related
- Bosonic String Amplitudes From Ribbon Graphs
- General Form Factors from String Amplitudes
- Scattering Equations as the lowest order K-identities in the calculation of Stringy Scaling of Hard String Scattering Amplitudes
- High-energy uniqueness of open-string disk integrals
- String Amplitudes on Integer Rectangles
BibTeX
@misc{huang2026infrared,
title = {{Infrared Consistency and the Uniqueness of String Amplitudes}},
author = {Yu-tin Huang and Shi-Lin Wan and Zhuo-Hui Wang and Shuang-Yong Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02124},
eprint = {2610.02124},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02124},
}
RIS
TY - UNPB
TI - Infrared Consistency and the Uniqueness of String Amplitudes
AU - Yu-tin Huang
AU - Shi-Lin Wan
AU - Zhuo-Hui Wang
AU - Shuang-Yong Zhou
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02124
UR - https://arxiv.org/abs/2610.02124
AB - Recent work has shown that maximal supersymmetry, combined with a particular scalar-parity condition at six points, imposes nonlinear constraints on four-point effective field theory amplitudes. Numerical bootstrap studies incorporating unitarity provide evidence for the Veneziano amplitude in maximally supersymmetric Yang--Mills theory and for the Virasoro--Shapiro amplitude, together with infinite-spin alternatives, in supergravity. In this paper, we establish these constraints to all orders in the low-energy expansion. The derivation uses a collinear limit in which three three-particle factorization channels, or six in gravity, simultaneously go on shell. A scalar-parity projection and a single discrete R-symmetry eliminate the unknown six-point remainder, leaving three-term master equations determined entirely by four-point factorization. Solving these equations proves the conjectured exponential forms and provides a map that reconstructs the full amplitude from its regular forward limit. Under explicit analytic and positive dispersive assumptions, the fixed reflection-even part of the gauge-theory exponential determines the forward spectral measure and uniquely selects the Veneziano amplitude, with finite-spin residues emerging as a consequence. In gravity, the exponential leaves the forward measure undetermined: a measure supported at a single massive level reconstructs an amplitude with infinitely many exchanged spins at that mass. Finite-spin support at the lowest massive pole is therefore an additional assumption required to select the Virasoro--Shapiro amplitude within the stated ultraviolet framework.
ER -