标题： Ads中的回路：从谱表示到位置空间III 显示英文标题

标题： Loops in AdS: From the Spectral Representation to Position Space III

摘要： 我们通过谱表示研究反德西特空间中的圈振幅。 我们考虑自旋场的圈图，特别是规范场，并推导出连接不同圈图族的各种恒等式，涉及不同的圈数、不同的自旋和不同的质量。 这些恒等式对于Witten图计算很有用。 考虑定义在AdS空间上的大-$N_f$共形标量QED理论，我们在$\frac{1}{N_f}$次领头阶推导出精确的4点关联函数的解析表达式。 此外，我们为各种“块状图”族的2点函数和边界4点函数推导了解析表达式。 最后，我们研究带有自旋场的4点梯子图，并推导出$k$-圈梯子图谱表示的积分表达式。 显示英文摘要

摘要： We study loop amplitudes in anti de-Sitter space via the spectral representation. We consider loops of spinning fields and in particular gauge fields, and derive various identities connecting different families of loop diagrams, at different number of loops, different spins, different masses. Such identities are useful for the computation of Witten diagrams. Considering the theory of large-$N_f$ conformal scalar QED defined on AdS space, we derive an analytic expression for the exact 4-point correlation function at sub-leading order in $\frac{1}{N_f}$. Additionally, we derive analytic expressions for bulk 2-point functions and boundary 4-point functions for various families of diagrams, which we denote as ``blob diagrams''. Finally we study 4-point ladder diagrams with spinning fields, and we derive integral expressions for the spectral representation of a $k$-loop ladder diagram.