巨引力子关联函数的负秩关系
Negative Rank Relations for Giant Graviton Correlators
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中文总结 AI 辅助
本文证明巨引力子与双巨引力子关联函数间存在由杨图转置引起的负秩反射关系，该关系在有限N自由关联函数中精确成立，并可推广至任意圈阶及任意Schur多项式外线算符。
中文摘要 AI 辅助
我们研究了$\mathcal N=4$超杨-米尔斯理论中巨引力子和双巨引力子的关联函数。尽管这两个对象对应于$AdS_5\times S^5$中相当不同的D3膜构型，它们的规范理论算符是与转置杨图相关联的Schur多项式。我们证明这种转置在关联函数层面上伴随着形式秩反射$N\to -N$。对于$U(N)$和$SU(N)$，该关系在有限$N$下的自由关联函数中是精确的，并且通过拉格朗日插入，扩展到每个圈阶的分离点弱耦合积分核。更一般地，它适用于任意数量的Schur多项式外线算符，前提是所有杨图都被转置。我们通过几个例子说明了这一关系，并讨论了其扩展到微扰积分核之外的证据。
英文摘要
We study correlation functions of giant and dual giant gravitons in $\mathcal N=4$ super Yang--Mills theory. Although the two objects correspond to rather different D3 brane configurations in $AdS_5\times S^5$, their gauge theory operators are Schur polynomials associated with transposed Young diagrams. We show that this transposition is accompanied by a formal rank reflection $N\to -N$ at the level of correlation functions. For both $U(N)$ and $SU(N)$, the relation is exact for free correlators at finite $N$, and, using Lagrangian insertion, extends to separated point weak coupling integrands at every loop order. More generally, it applies to any number of Schur polynomial external operators, provided all Young diagrams are transposed. We illustrate the relation in several examples and also discuss evidence for its extension beyond perturbative integrands.
