$\mathcal N =1$ 超对称中的正性界
Positivity Bounds in $\mathcal N =1$ Supersymmetry
- Fudan University（复旦大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文在 N=1 超对称中扩展正性界 bootstrap，利用超对称 Ward 恒等式关联不同过程的 Wilson 系数，明确展示维度-8 算符下标量、费米子与规范场四次相互作用的正性约束及其相互依赖。
中文摘要 AI 辅助
对于一个低能有效场论（EFT）要允许存在一致的紫外（UV）完备化，它必须遵循定域性、幺正性、解析性和洛伦兹不变性等基本原理。这通过 $2\rightarrow2$ 前向弹性振幅的色散关系对某些 Wilson 系数施加正性约束，这些约束对理论一致性和实验现象学都具有重要意义。在本工作中，我们将这一 bootstrap 框架扩展到 $\mathcal N = 1$ 超对称理论，其中超庞加莱代数将单个超多重态中的玻色子和费米子自由度联系起来。超对称 Ward 恒等式（SWIs）强制分量散射振幅之间满足精确的线性关系。因此，与不同 $2\rightarrow2$ 过程相关的 Wilson 系数相互约束，使得它们的正性界相互依赖。聚焦于维度为 8 的算符，我们明确展示了涉及标量、费米子和规范场的四次相互作用的正性界，并演示了它们如何作为 SWIs 的直接结果而相互关联。此外，我们预期该框架的代数性质自然延伸到圈级超振幅和高点过程，为超对称 EFT 提供统一的 bootstrap 视角。
英文摘要
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.
