论文标题
在四个维度上的多条埃姆振幅的注释
A note on multi-trace EYM amplitudes in four dimensions
论文作者
论文摘要
在四个维度中，树级双轨爱因斯坦 - 杨米尔（EYM）幅度（EYM）幅度具有两个负helicity gluons（$（g^ - ，g^ - ）$ - 配置）满足了对称跨度的森林公式，这是从图形扩展规则中得出的。另一方面，在Cachazo-He-Yuan（CHY）公式的框架中，最大甲基侵入性（MHV）幅度由散射方程的MHV解决方案支持。双向振幅的对称公式与Cachazo-He-Yuan（Chy）公式的MHV扇区之间的关系仍然不清楚。在本说明中，我们在四个维度上促进了跨越森林的一系列转变，然后展示了分解双轨EYM振幅CHY公式的MHV扇区的系统方法。沿着这条线，双轨MHV振幅的对称公式直接由CHY公式的MHV扇区获得。然后，我们证明，当负 - （或阳性）螺旋性胶子的数量小于痕迹的数量时，具有任意总颗粒总数（重力和胶子）的EYM幅度必须消失。
In four dimensions, a tree-level double-trace Einstein-Yang-Mills (EYM) amplitude with two negative-helicity gluons (the $(g^-,g^-)$-configuration) satisfies a symmetric spanning forest formula, which was derived from the graphic expansion rule. On another hand, in the framework of Cachazo-He-Yuan (CHY) formula, the maximally-helicity-violating (MHV) amplitudes are supported by the MHV solution of scattering equations. The relationship between the symmetric formula for double-trace amplitudes, and the MHV sector of Cachazo-He-Yuan (CHY) formula in four dimensions is still not clear. In this note, we promote a series of transformations of the spanning forests in four dimensions and then show a systematic way for decomposing the MHV sector of the CHY formula of double-trace EYM amplitudes. Along this line, the symmetric formula of double-trace MHV amplitudes is directly obtained by the MHV sector of CHY formula. We then prove that EYM amplitude with an arbitrary total number of negative-helicity particles (gravitons and gluons) has to vanish when the number of negative- (or positive-) helicity gluons is less than the number of traces.
