Publications by authors named "Tomasz Lukowski"
In this Letter, we define the Aharony-Bergman-Jafferis-Maldacena loop momentum amplituhedron, which is a geometry encoding Aharony-Bergman-Jafferis-Maldacena planar tree-level amplitudes and loop integrands in the three-dimensional spinor helicity space. Translating it to the space of dual momenta produces a remarkably simple geometry given by configurations of spacelike separated off-shell momenta living inside a curvy polytope defined by momenta of scattered particles. We conjecture that the canonical differential form on this space gives amplitude integrands, and we provide a new formula for all one-loop n-particle integrands in the positive branch.
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- - This paper explores the connection between two mathematical frameworks called the momentum amplituhedron (related to scattering amplitudes in a specific gauge theory) and the kinematic associahedron (pertaining to amplitudes in a bi-adjoint scalar theory).
- - The research shows how restricting the kinematic associahedron to four dimensions reveals a direct relationship with the momentum amplituhedron's canonical form, especially after accounting for certain scaling dependencies.
- - The study uncovers shared singularity structures in both frameworks, indicating that their amplitude behaviors around specific conditions are akin, while also detailing the kinematic spaces for these theories when limited to four dimensions.
Planar N = 4 supersymmetric Yang-Mills theory appears to be integrable. While this allows one to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter.
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