论文标题
MHV重力散射振幅和天体上的当前代数
MHV Graviton Scattering Amplitudes and Current Algebra on the Celestial Sphere
论文作者
论文摘要
Cachazo-strominger subleding soft Graviton定理用于正螺旋软吸引力等同于$ \ overline {sl（2，\ mathbb c）} $电流的病房身份。这自然会产生$ \叠加{sl（2，\ mathbb c）} $当前的代数生活在天体球上。 $ \叠加{sl（2，\ mathbb c）} $当前代数和超级翻译的发电机，来自正螺旋的前导软吸引力，形成了一个封闭的代数。我们发现，从MHV振幅中提取的天体CFT中两个重力原则的OPE是根据该代数完全确定的。更确切地说，1）OPE中的跨标准术语是根据领先的OPE系数确定的，如果我们要求OPE的两侧在此局部对称代数下以相同的方式转换。 2）阳性螺旋性引力在该局部代数下的零状态，其脱钩会导致MHV振幅的微分方程。 $ n $ point MHV振幅满足了两个系统的$（n-2）$线性一阶PDE，对应于$（n-2）$阳性螺旋力重力。我们已经使用Hodges的公式检查了一个微分方程系统，都可以通过任何MHV振幅满足，而另一个系统已被检查多达六个Graviton MHV振幅。 3）可以从这些微分方程中确定领先的OPE系数。 这指出了天体CFT的一个自主部门的存在，该区域全息计算MHV Graviton散射幅度，并由该局部对称性代数完全定义。天体CFT的MHV领域就像$ 2 $ -D CFT的最小型号。
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.
