AdS$_2$中费曼图展开的约化技术
Reduction technique for expanding the Feynman diagrams in AdS$_2$
- I.E. Tamm Department of Theoretical Physics, P.N. Lebedev Physical Institute（P.N. 列别捷夫物理研究所 I.E. 塔姆理论物理系）
- Moscow Institute of Physics and Technology（莫斯科物理技术学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出一种约化技术，将AdS$_2$中任意n点费曼树图展开为Wilson线网络，复杂度不随n增加，并应用于五点图，重现了Witten图分解为共形块的已知结果。
AI中文摘要：
我们提出了将二维AdS空间中n点费曼图展开为Wilson线网络的约化技术。该技术适用于任意n点树图，将其表示为若干Wilson线网络算子矩阵元级数，并利用(n-1)点AdS费曼图的Wilson网络展开，这些展开可通过同一技术获得。因此，只要已知(n-1)点图的展开，该技术的复杂度不随n增加。为演示此约化技术，我们将其应用于所有拓扑不同的五点AdS费曼树图。在共形边界附近的展开重现了相应五点Witten图分解为共形块的已知结果。
英文摘要：
We formulate the reduction technique for expanding the $n$-point AdS Feynman diagrams in two dimensions into the Wilson line networks. The technique applies to any $n$-point tree diagram, expressing it as several series of the matrix elements of Wilson line network operators, and employs the Wilson network expansions of the $(n-1)$-point AdS Feynman diagrams, which can in turn be obtained using the same technique. Consequently, the complexity of this technique does not increase with $n$, provided that the expansions of the $(n-1)$-point diagrams are known. To demonstrate the reduction technique, we apply it to all topologically distinct five-point AdS Feynman tree diagrams. The resulting expansions near the conformal boundary reproduce the known decompositions of the corresponding five-point Witten diagrams into conformal blocks.
