arXiv 2505.239482025-05hep-th

AdS中的极值耦合、引力子交换与胶子散射

Extremal couplings, graviton exchange, and gluon scattering in AdS

Shai M. Chester, Rishi Mouland, Jesse van Muiden

备注：: 29 pages plus appendices, 1 figure, v2 submitted for publication

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AI总结：

本文研究了AdS中带七膜奇点的IIB型弦理论对偶理论，计算了引力子与胶子模间的极值耦合，利用引力子交换项解释了发散的3点图，并结合超对称局域化完全固定了特定4d $\mathcal{N}=2$规范理论在$1/N^2$阶的全息关联函数。

摘要：

AdS中的极值三次耦合关联了满足$Δ_i+Δ_j=Δ_k$的体场。此类耦合导致发散的3点Witten图，且不出现在具有最大超对称性的理论中。我们考虑此类耦合非零的最简单理论，即带有$N$个D3膜探测七膜各种位形的IIB型弦理论，它们对偶于特定的4d $\mathcal{N}=2$ SCFTs。在大$N$下，低能有效理论是带奇点的$AdS_5\times S^5$上的超引力，其奇点固定点轨迹为$AdS_5\times S^3$。这些理论具有无限塔的引力子模和七膜上的胶子模。我们计算了这些模之间非零的耦合，其通常为（超）极值的。我们利用这些耦合计算了胶子KK模全息关联函数$\langle22pp\rangle$中的引力子交换项，该项出现在与1圈胶子交换相同的$1/N^2$阶，并接收整个引力子模塔的贡献。我们利用该引力子交换项计算了单迹引力子模与胶子模双迹的去混合，这解释了发散的3点图。最后，针对最简单4d $\mathcal{N}=2$规范理论的$\langle 2222\rangle$，我们利用超对称局域化和新的引力子交换项完全确定了$1/N^2$阶的关联函数。

英文摘要：

Extremal cubic couplings in AdS relate bulk fields such that $Δ_i+Δ_j=Δ_k$. Such couplings lead to divergent 3-point Witten diagrams, and do not occur in theories with maximal supersymmetry. We consider the simplest theories where such coupling are non-zero, which is type IIB string theory with $N$ D3 branes probing various configurations of sevenbranes, which are dual to certain 4d $\mathcal{N}=2$ SCFTs. At large $N$, the low energy effective theory is supergravity on $AdS_5\times S^5$ with a singularity, whose fixed point locus is $AdS_5\times S^3$. These theories have infinite towers of graviton modes, as well as gluon modes on the sevenbranes. We compute the nonzero coupling between these modes, which is in general (super)-extremal. We use these couplings to compute the graviton exchange term in the holographic correlator of gluon KK modes $\langle22pp\rangle$, which appears at the same order $1/N^2$ as 1-loop gluon exchange, and receives contributions from a whole tower of graviton modes. We use this graviton exchange term to compute the unmixing of the single trace graviton modes with double traces of gluon modes, which explains the divergent 3-point diagrams. Finally, for $\langle 2222\rangle$ for the simplest 4d $\mathcal{N}=2$ gauge theory, we use supersymmetric localization and the new graviton exchange term to completely fix the correlator at order $1/N^2$.

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