All-multiplicity completion of maximally supersymmetric gauge amplitudes
Abstract
We show that the known six-point constraints on four-point amplitudes are sufficient for completion at arbitrary multiplicity in planar, four-dimensional maximally supersymmetric gauge theory. We construct massless tree amplitudes as formal series in the derivative expansion, with the standard supersymmetric Yang-Mills three-point amplitudes, unbroken R-symmetry, and parity invariance of amplitudes with only external scalars, holding the scalar labels fixed. For a positive leading four-point contact coefficient, the even coefficients in the logarithmic parameterization are fixed, while every real sequence of odd coefficients is realized by a completion at all derivative orders. The construction uses the field-theory Kawai-Lewellen-Tye bilinear and normalized matrices of sphere integrals. Exponentiating homogeneous components of their matrix logarithms varies the odd coefficients independently while preserving locality and factorization through the complete massless multiplet. The six-point conditions are therefore necessary and sufficient for such a completion. Higher-multiplicity consistency imposes no further restrictions on these four-point coefficients once the higher-point contact interactions are chosen consistently with the same symmetries and factorization conditions.
Related
- Vacuum Structure of Maximally Supersymmetric Two-Dimensional Gauge Theories
- Anomaly- and Tadpole-Compatible Fermion Completion of Six-Dimensional SU(4) Gauge-Higgs Unification (Part I)
- Non-supersymmetric dualities beyond the gauge algebra
- Perturbative Holonomy Potentials and Vacua in Chiral Supersymmetric Gauge Theories
- Quantum Elliptic Cohomology From Four-Dimensional Minimal Supersymmetric Gauge Theories
BibTeX
@misc{sung2026allmultiplicity,
title = {{All-multiplicity completion of maximally supersymmetric gauge amplitudes}},
author = {Ilmo Sung},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.10712},
eprint = {2610.10712},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.10712},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - All-multiplicity completion of maximally supersymmetric gauge amplitudes
AU - Ilmo Sung
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2610.10712
UR - https://arxiv.org/abs/2610.10712
AB - We show that the known six-point constraints on four-point amplitudes are sufficient for completion at arbitrary multiplicity in planar, four-dimensional maximally supersymmetric gauge theory. We construct massless tree amplitudes as formal series in the derivative expansion, with the standard supersymmetric Yang-Mills three-point amplitudes, unbroken R-symmetry, and parity invariance of amplitudes with only external scalars, holding the scalar labels fixed. For a positive leading four-point contact coefficient, the even coefficients in the logarithmic parameterization are fixed, while every real sequence of odd coefficients is realized by a completion at all derivative orders. The construction uses the field-theory Kawai-Lewellen-Tye bilinear and normalized matrices of sphere integrals. Exponentiating homogeneous components of their matrix logarithms varies the odd coefficients independently while preserving locality and factorization through the complete massless multiplet. The six-point conditions are therefore necessary and sufficient for such a completion. Higher-multiplicity consistency imposes no further restrictions on these four-point coefficients once the higher-point contact interactions are chosen consistently with the same symmetries and factorization conditions.
ER -