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arXiv 2007.06574hep-th
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AdS中的散射方程：任意维标量关联函数

Scattering Equations in AdS: Scalar Correlators in Arbitrary Dimensions

Lorenz Eberhardt, Shota Komatsu, Sebastian Mizera

备注：
44 pages; v2 References added. Modified discussion of anomalies in sections 2 and 3. Main results unchanged
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摘要：

在AdS空间中引入玻色定界弦论。尽管该理论在量子水平上是反常的，但人们仍然可以在经典极限下使用它来导出任意时空维中边界CFT算子的关联函数的新公式。由此产生的结构可以被视为CHY形式主义的平坦空间S-矩阵的自然扩展，因为它类似地表示AdS中的树级振幅作为具有穿孔的黎曼球的模空间上的积分。这些积分本地化的散射方程，我们直接从陪集流形上的ambitwistor字符串作用的算子值的版本。作为这种形式主义的测试场，我们专注于最简单的情况下，ambitwistor字符串耦合到两个当前代数，这使得双伴随标量关联函数在AdS。为了直接计算它们，我们利用一系列的轮廓变形的模空间的穿孔黎曼球和检查的结果符合树级Witten图计算的所有重数。我们还开始研究AdS中的散射方程的本征函数，该本征函数在不同的OPE通道中的共形分波之间插值，并指出与Calogero-Sutherland模型的椭圆变形的连接。

英文摘要：

We introduce a bosonic ambitwistor string theory in AdS space. Even though the theory is anomalous at the quantum level, one can nevertheless use it in the classical limit to derive a novel formula for correlation functions of boundary CFT operators in arbitrary space-time dimensions. The resulting construction can be treated as a natural extension of the CHY formalism for the flat-space S-matrix, as it similarly expresses tree-level amplitudes in AdS as integrals over the moduli space of Riemann spheres with punctures. These integrals localize on an operator-valued version of scattering equations, which we derive directly from the ambitwistor string action on a coset manifold. As a testing ground for this formalism we focus on the simplest case of ambitwistor string coupled to two current algebras, which gives bi-adjoint scalar correlators in AdS. In order to evaluate them directly, we make use of a series of contour deformations on the moduli space of punctured Riemann spheres and check that the result agrees with tree level Witten diagram computations to all multiplicity. We also initiate the study of eigenfunctions of scattering equations in AdS, which interpolate between conformal partial waves in different OPE channels, and point out a connection to an elliptic deformation of the Calogero-Sutherland model.

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