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arXiv 2008.04330hep-th
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天球上的MHV引力子散射振幅和电流代数

MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere

Shamik Banerjee, Sudip Ghosh, Partha Paul

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摘要：

正螺旋度软引力子的Cachazo-Strominger次引导软引力子定理等价于$\overline{SL(2,\mathbb C)}$流的Ward恒等式。这自然会产生一个生活在天球上的PDMATHAMM电流代数。$\overline{SL(2,\mathbb C)}$流代数的生成元与正螺旋度主导的软引力子的超平移形成一个闭代数。我们发现，从MHV振幅中提取的天体CFT中两个引力子原色的OPE完全由这个代数确定。更精确地说，1）如果我们要求OPE的两侧在这个局部对称代数下以相同的方式变换，则OPE中的子前导项根据前导OPE系数来确定。2)正螺旋引力子在这个局部代数下具有零态，其解耦导致MHV振幅的微分方程。一个$n$点MHV振幅满足对应于$(n-2)$正螺旋度引力子的两个$(n-2)$线性一阶偏微分方程组。我们已经使用霍奇斯公式检查了一个微分方程组满足任何MHV振幅，而另一个系统已经检查了高达六个引力子MHV振幅。3)人们可以从这些微分方程中确定领先的OPE系数。这表明天体CFT存在一个自治扇区，它全息计算MHV引力子散射振幅，并完全由这个局部对称代数定义。天体CFT的MHV扇区就像是$2$-D CFT的最小模型。

英文摘要：

The Cachazo-Strominger subleading soft graviton theorem for a positive helicity soft graviton is equivalent to the Ward identities for $\overline{SL(2,\mathbb C)}$ currents. This naturally gives rise to a $\overline{SL(2,\mathbb C)}$ current algebra living on the celestial sphere. The generators of the $\overline{SL(2,\mathbb C)}$ current algebra and the supertranslations, coming from a positive helicity leading soft graviton, form a closed algebra. We find that the OPE of two graviton primaries in the Celestial CFT, extracted from MHV amplitudes, is completely determined in terms of this algebra. To be more precise, 1) The subleading terms in the OPE are determined in terms of the leading OPE coefficient if we demand that both sides of the OPE transform in the same way under this local symmetry algebra. 2) Positive helicity gravitons have null states under this local algebra whose decoupling leads to differential equations for MHV amplitudes. An $n$ point MHV amplitude satisfies two systems of $(n-2)$ linear first order PDEs corresponding to $(n-2)$ positive helicity gravitons. We have checked, using Hodges' formula, that one system of differential equations is satisfied by any MHV amplitude, whereas the other system has been checked up to six graviton MHV amplitude. 3) One can determine the leading OPE coefficients from these differential equations. This points to the existence of an autonomous sector of the Celestial CFT which holographically computes the MHV graviton scattering amplitudes and is completely defined by this local symmetry algebra. The MHV-sector of the Celestial CFT is like a minimal model of $2$-D CFT.

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