论文标题
大型$ P $探索。从Sugra到Mellin空间中的大弦
Large $p$ explorations. From SUGRA to big STRINGS in Mellin space
论文作者
论文摘要
我们探索了一种探测$ ads_5 \ times s^5 $的闭合字符串散射的新方法，我们称之为“大$ p $ limit”。它包括在$ \ mathcal {n}中研究单粒子操作员的四点相关器，从$ n $上讲，$ n $和大't Hooft耦合$λ$，通过查看双kk模式变为短符号的策略，以$ n $ $ n $。在此制度中，单粒子运算符的电荷为$λ^{1/4} $的顺序，并且双KK模式在字段和字符串之间。从Sugra开始，我们通过引入改进的$ ads_5 \ times s^5 $ mellin空间幅度来计算相关器的大$ p $限制，我们表明相关器由鞍点主导。我们的结果与从$ ads_5 \ times s^5 $的边界射击的四个测量学射击的图片是一致的，在一个共同的散装点上，它们像在平坦的空间一样散布。 Mandelstam不变性与Mellin变量相对应，然后与交叉比例的某些组合。在马鞍点，相关器的动力学与散装的梅林振幅直接相关，在占用大$ p $的过程中，这成为平坦的空间十维s-matrix。因此，我们学习了如何在$ ads_5 \ times s^5 $ mellin振幅中嵌入完整的IIB S-MATRIX，以及如何将后者分层为大$ P $扩展。我们计算当前可用的所有零属数据的大$ p $限制，指出了已知结果的其他隐藏简单性。然后，我们证明，零$ p $的零属自然会导致散装点周围最小面积表面的总膜阶段。在一环，我们首先发现了一个小说且有限的梅林振幅，然后我们表明，大$ p $限制了重力S-Matrix的精美渐近。
We explore a new way of probing scattering of closed strings in $AdS_5\times S^5$, which we call `the large $p$ limit'. It consists of studying four-point correlators of single-particle operators in $\mathcal{N}=4$ SYM at large $N$ and large 't Hooft coupling $λ$, by looking at the regime in which the dual KK modes become short massive strings. In this regime the charge of the single-particle operators is order $λ^{1/4}$ and the dual KK modes are in between fields and strings. Starting from SUGRA we compute the large $p$ limit of the correlators by introducing an improved $AdS_5\times S^5$ Mellin space amplitude, and we show that the correlator is dominated by a saddle point. Our results are consistent with the picture of four geodesics shooting from the boundary of $AdS_5\times S^5$ towards a common bulk point, where they scatter as if they were in flat space. The Mandelstam invariants are put in correspondence with the Mellin variables and in turn with certain combinations of cross ratios. At the saddle point the dynamics of the correlator is directly related to the bulk Mellin amplitude, which in the process of taking large $p$ becomes the flat space ten-dimensional S-matrix. We thus learn how to embed the full type IIB S-matrix in the $AdS_5\times S^5$ Mellin amplitude, and how to stratify the latter in a large $p$ expansion. We compute the large $p$ limit of all genus zero data currently available, pointing out additional hidden simplicity of known results. We then show that the genus zero resummation at large $p$ naturally leads to the Gross-Mende phase for the minimal area surface around the bulk point. At one-loop, we first uncover a novel and finite Mellin amplitude, and then we show that the large $p$ limit beautifully asymptotes the gravitational S-matrix.
