Pair-zero and degree conditions admit extra six-dimensional hook solutions at seven points and a two-dimensional plane at eight; Bose symmetry and one normalized physical boundary condition single out the Hodges numerator.
Note on solutions of scattering equations
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abstract
In the CHY-frame for the amplitudes, there are two kinds of singularities we need to deal with. The first one is the pole singularities when the kinematics is not general, such that some of $S_A\to 0$. The second one is the collapse of locations of points after solving scattering equations (i.e., the singular solutions). These two types of singularities are tightly related to each other, but the exact mapping is not well understood. In this paper, we have initiated the systematic study of the mapping. We have demonstrated the different mapping patterns using three typical situations, i.e., the factorization limit, the soft limit and the forward limit.
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Algebraic versus physical uniqueness of MHV gravity numerators
Pair-zero and degree conditions admit extra six-dimensional hook solutions at seven points and a two-dimensional plane at eight; Bose symmetry and one normalized physical boundary condition single out the Hodges numerator.