Abstract
We present the building blocks that can be combined to produce tree-level S-matrix elements of a variety of theories with various spins mixed in arbitrary dimensions. The new formulas for the scattering of n massless particles are given by integrals over the positions of n points on a sphere restricted to satisfy the scattering equations. As applications, we obtain all single-trace amplitudes in Einstein-Yang-Mills (EYM) theory, and generalizations to include scalars. Also in EYM but extended by a B-field and a dilaton, we present all double-trace gluon amplitudes. The building blocks are made of Pfaffians and Parke-Taylor-like factors of subsets of particle labels.
Highlights
We present the building blocks that can be combined to produce tree-level Smatrix elements of a variety of theories with various spins mixed in arbitrary dimensions
A type II version leads to a consistent theory with correlators that compute scattering amplitudes of gravitons in a form that matches exactly the CHY formula
The main result of this work is a formula for the single trace amplitude of r gluons and s gravitons (n = r + s) in Einstein-Yang-Mills (EYM) theory: IrE,sYM = Cr E(ǫr+1, ǫr+2, . . . , ǫn) E(ǫ1, ǫ2, . . . , ǫn) where Cr is given by (1.5) but only for particles {1, 2, . . . , r}, and the precise form of E(ǫr+1, ǫr+2, . . . , ǫn) will be given
Summary
The first set of building blocks is obtained by considering a subset S = {i1, i2, . The second set of building blocks is defined for a given subset S. In this case one defines an anti-symmetric 2r × 2r matrix, ΨS, as follows. In the case r = n − 1 we define E = 0 and when r = n we use the definition given in [1]. The correct definition of E is the so-called reduced Pfaffian. It was proven in [1] that (2.7) is independent of the choice of {i, j}. This is the object that appears in the formulas, (1.4), for pure Yang-Mills and pure gravity presented in the Introduction
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