论文标题
全环四点Aharony-Bergman-Jafferis-Maldacena振幅，从尺寸降低的Amplituhedron
All-Loop Four-Point Aharony-Bergman-Jafferis-Maldacena Amplitudes from Dimensional Reduction of the Amplituhedron
论文作者
论文摘要
我们定义了从$ {\ cal n} = 4 $ sym中从全环amplituhedron获得的新几何形状，通过将其四维外部和环动量减少到三个维度。我们提供了最简单的四点案例，我们提供了有力的证据表明，这种规范形式``减少的Amplituhedron''给ABJM四个四点振幅的全循环整合。除了几何表现出的各种全面削减外，我们还为整合均具有明确的新成果，而不是五个loops noperand nemerand nemerand noseand noseand n of pos not $ simple n $ cal $ n $。这样的全环简化的原因是，所谓的负几何形状的一小部分在尺寸还原上幸存下来，这对应于两部分图。
We define a new geometry obtained from the all-loop amplituhedron in ${\cal N}=4$ SYM by reducing its four-dimensional external and loop momenta to three dimensions. Focusing on the simplest four-point case, we provide strong evidence that the canonical form of this ``reduced amplituhedron" gives the all-loop integrand of the ABJM four-point amplitude. In addition to various all-loop cuts manifested by the geometry, we present explicitly new results for the integrand up to five loops, which are much simpler than results in ${\cal N}=4$ SYM. One of the reasons for such all-loop simplifications is that only a very small fraction of the so-called negative geometries survive the dimensional reduction, which corresponds to bipartite graphs. Our results suggest an unexpected relation between four-point amplitudes in these two theories.
