Positivity Bounds in $\mathcal N =1$ 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 $2\rightarrow2$ forward elastic amplitudes, which carry significant implications for both theoretical consistency and experimental phenomenology. In this work, we extend this bootstrap framework to $\mathcal N = 1$ supersymmetric theories, where the super-Poincaré 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 $2\rightarrow2$ 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.