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Award ID contains: 2111943

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  1. ; (, Journal of High Energy Physics)
    A<sc>bstract</sc> In the decomposition of gauge-theory amplitudes into kinematic and color factors, the color factors (at a given loop orderL) span a proper subspace of the extended trace space (which consists of single and multiple traces of generators of the gauge group, graded by powers ofN). Using an iterative process, we systematically construct theL-loop color space of four-point amplitudes of fields in the adjoint representation of SU(N), SO(N), or Sp(N). We define the null space as the orthogonal complement of the color space. For SU(N), we confirm the existence of four independent null vectors (forL≥ 2) and for SO(N) and Sp(N), we establish the existence of seventeen independent null vectors (forL≥ 5). Each null vector corresponds to a group-theory constraint on the color-ordered amplitudes of the gauge theory. 
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  2. (, Journal of High Energy Physics)
    A bstract Color-factor symmetry is a property of tree-level gauge-theory amplitudes containing at least one gluon. BCJ relations among color-ordered amplitudes follow directly from this symmetry. Color-factor symmetry is also a feature of biadjoint scalar theory amplitudes as well as of their equations of motion. In this paper, we present a new proof of color-factor symmetry using a recursive method derived from the perturbiner expansion of the classical equations of motion. 
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  3. ; (, Journal of High Energy Physics)
    A bstract A previously proposed all-loop-orders relation between the Regge limits of four-point amplitudes of $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory and $$ \mathcal{N} $$ N = 8 supergravity is established at the three-loop level. We show that the Regge limit of known expressions for the amplitudes obtained using generalized unitarity simplifies in both cases to a (modified) sum over three-loop ladder and crossed-ladder scalar diagrams. This in turn is consistent with the result obtained using the eikonal representation of the four-point gravity amplitude. A possible exact three-loop relation between four-point amplitudes is also considered. 
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