Positivity Bounds in š¯’© =1 Supersymmetry
Abstract
For a low-energy Effective Field Theory (EFT) to admit a consistent ultraviolet (UV) completion, it must adhere to the fundamental principles of locality, unitarity, analyticity, and Lorentz invariance. This leads to positivity constraints on certain Wilson coefficients via dispersion relations of 2ā†’2 forward elastic amplitudes, which carry significant implications for both theoretical consistency and experimental phenomenology. In this work, we extend this bootstrap framework to š¯’© = 1 supersymmetric theories, where the super-PoincarĆ© algebra relates the bosonic and fermionic degrees of freedom within a single supermultiplet. Supersymmetric Ward identities (SWIs) enforce exact linear relations among component scattering amplitudes. Consequently, the Wilson coefficients associated with different 2ā†’2 processes are mutually constrained, rendering their respective positivity bounds dependent. Focusing on dimension-8 operators, we explicitly show the positivity bounds on quartic interactions involving scalars, fermions and gauge fields, and demonstrate how they are related as a direct consequence of the SWIs. Furthermore, we expect that the algebraic nature of this framework naturally extends to loop-level superamplitudes and higher-point processes, providing a unified bootstrap perspective on supersymmetric EFTs.
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BibTeX
@misc{bu2026positivity,
title = {{Positivity Bounds in $\mathcal N =1$ Supersymmetry}},
author = {Jingxuan Bu and Jiayin Gu and Runqing Wang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.16924},
eprint = {2609.16924},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.16924},
}
RIS
TY - UNPB
TI - Positivity Bounds in š¯’© =1 Supersymmetry
AU - Jingxuan Bu
AU - Jiayin Gu
AU - Runqing Wang
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.16924
UR - https://arxiv.org/abs/2609.16924
AB - For a low-energy Effective Field Theory (EFT) to admit a consistent ultraviolet (UV) completion, it must adhere to the fundamental principles of locality, unitarity, analyticity, and Lorentz invariance. This leads to positivity constraints on certain Wilson coefficients via dispersion relations of 2ā†’2 forward elastic amplitudes, which carry significant implications for both theoretical consistency and experimental phenomenology. In this work, we extend this bootstrap framework to š¯’© = 1 supersymmetric theories, where the super-PoincarĆ© algebra relates the bosonic and fermionic degrees of freedom within a single supermultiplet. Supersymmetric Ward identities (SWIs) enforce exact linear relations among component scattering amplitudes. Consequently, the Wilson coefficients associated with different 2ā†’2 processes are mutually constrained, rendering their respective positivity bounds dependent. Focusing on dimension-8 operators, we explicitly show the positivity bounds on quartic interactions involving scalars, fermions and gauge fields, and demonstrate how they are related as a direct consequence of the SWIs. Furthermore, we expect that the algebraic nature of this framework naturally extends to loop-level superamplitudes and higher-point processes, providing a unified bootstrap perspective on supersymmetric EFTs.
ER -