Gauge/gravity correspondence is regarded as a powerful tool for the study of strongly coupled quantum systems, but its proof is not available. An unresolved issue that should be closely related to the proof is what kind of correspondence exists, if any, when gauge theory is weakly coupled. We report progress about this limit for the case associated with D|$p$|-branes (⁠|$0\le p\le 4$|⁠), namely, the duality between the |$(p+1)$|D maximally supersymmetric Yang–Mills theory and superstring theory on the near-horizon limit of the D|$p$|-brane solution. It has been suggested by supergravity analysis that the two-point functions of certain operators in gauge theory obey a power law with the power different from the free-field value for |$p\neq 3$|⁠. In this work, we show for the first time that the free-field result can be reproduced by superstring theory on the strongly curved background. The operator that we consider is of the form |${\rm Tr}(Z^J)$|⁠, where |$Z$| is a complex combination of two scalar fields. We assume that the corresponding string has the worldsheet spatial direction discretized into |$J$| bits, and use the fact that these bits become non-interacting when ’t Hooft coupling is zero.

中文翻译：

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从D p射线的轨距/重力对应关系中弱耦合全息的证据

量规/重力对应被认为是研究强耦合量子系统的有力工具，但尚无其证明。应该与证明密切相关的一个未解决的问题是，当量表理论弱耦合时，存在什么样的对应关系（如果有）。对于与D | $ p $ |相关的情况，我们报告了有关此限制的进度 -branes（⁠| $ 0 \ le p \ le 4 $ |⁠），即| $（p + 1）$ |之间的对偶 d最大的超对称杨-米尔斯理论，在d的近范围限制超弦理论| $ P $ | 溶液。超重力分析表明，规范理论中某些算子的两点函数服从幂定律，其幂不同于自由场值。| $ p \ neq 3 $ |⁠。在这项工作中，我们首次展示了超场理论可以在强烈弯曲的背景上再现自由场结果。我们考虑的运算符的格式为| $ {\ rm Tr}（Z ^ J）$ |⁠，其中| $ Z $ | 是两个标量字段的复杂组合。我们假设相应的字符串的世界表空间方向离散为| $ J $ | 位，并使用以下事实：当't Hooft耦合为零时，这些位不相互作用。