走向高自旋全纯零形式扇区中的全阶局域性
Towards All-Order Locality in the Higher-Spin Holomorphic Zero-Form Sector
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中文总结 AI 辅助
本文针对Vasiliev方程导出的全纯零形式扇区，提出并验证了确保时空自旋局域性的条件，成功计算了自旋局域的$\eta^2$顶点，为高自旋理论的全阶局部顶点构建奠定基础。
中文摘要 AI 辅助
本文工作致力于从Vasiliev方程中得到的全纯零形式扇区中局部相互作用顶点的构建。我们关注一个对零形式顶点提出的要求，该要求先前在arXiv:2208.02004中以较弱的形式提出，该要求与旋量自旋局域性一起，保证了时空自旋局域性。我们推导出全纯一形式扇区顶点上的必要且充分条件，这些条件确保存在满足此要求的全纯零形式顶点。作为具体演示，所提出的方案被应用于计算自旋局域的holomorphic $\eta^2$ 零形式扇区顶点，这一结果超越了先前仅建立了旋量自旋局域性的工作。这些发现为在高自旋理论中系统地全阶构建局部顶点奠定了基础。
英文摘要
This work addresses the construction of local interaction vertices in the holomorphic zero-form sector obtained from Vasiliev equations. We focus on a requirement on zero-form vertices, previously proposed in a less restrictive form in arXiv:2208.02004, which, together with spinor spin-locality, guarantees space-time spin-locality. Necessary and sufficient conditions on the holomorphic one-form sector vertices are derived that ensure the existence of holomorphic zero-form vertices satisfying this requirement. As a concrete demonstration, the proposed scheme is applied to compute the spin-local holomorphic $η^2$ zero-form sector vertex, a result that goes beyond previous work where only spinor spin-locality was established. These findings lay the groundwork for a systematic all-order construction of local vertices in higher-spin theory.
发表机构
- I.E. Tamm Department of Theoretical Physics, Lebedev Physical Institute（列别杰夫物理研究所伊·叶·塔姆理论物理系）
- Moscow Institute of Physics and Technology（莫斯科物理技术学院）
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