论文标题
来自天电流代数的MHV Gluon散射振幅
MHV Gluon Scattering Amplitudes from Celestial Current Algebras
论文作者
论文摘要
我们表明，$ N $ - 点树水平MHV GLUON散射幅度的梅林变换（在纯Yang-Mills理论中也称为天体振幅）满足$（n-2）$线性一阶偏差方程的系统，与$（n-2）$阳性螺旋相对应。尽管这些方程与$ su（n）$当前代数的knizhnik-zamolodchikov方程非常相似，但也有一个来自转向的软gluon电流代数的额外的“校正”术语。这些方程可用于计算天体球体上的gluon-gluon ope中的领先术语。对于动量空间树级MHV散射幅度，也可以写下类似的方程式。我们还提出了一种处理未关闭当前代数发电机的方法的方法。然后，将其用于计算混合螺旋性Gluon OPE中的一些跨胶结项，我们的结果与使用Mellin MHV振幅从显式计算获得的结果相匹配。
We show that the Mellin transform of an $n$-point tree level MHV gluon scattering amplitude, also known as the celestial amplitude in pure Yang-Mills theory, satisfies a system of $(n-2)$ linear first order partial differential equations corresponding to $(n-2)$ positive helicity gluons. Although these equations closely resemble Knizhnik-Zamolodchikov equations for $SU(N)$ current algebra there is also an additional "correction" term coming from the subleading soft gluon current algebra. These equations can be used to compute the leading term in the gluon-gluon OPE on the celestial sphere. Similar equations can also be written down for the momentum space tree level MHV scattering amplitudes. We also propose a way to deal with the non closure of subleading current algebra generators under commutation. This is then used to compute some subleading terms in the mixed helicity gluon OPE and our results match with those obtained from an explicit calculation using the Mellin MHV amplitude.
