A systematic deformation theory for CEGM amplitudes yields generalized nonlinear sigma model amplitudes, with dimension gcd(k,n)-1 for pure deformations and an embedding of ordinary NLSM amplitudes as residues.
Minimal Kinematics on $\mathcal{M}_{0,n}$
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Minimal kinematics identifies likelihood degenerations where the critical points are given by rational formulas. These rest on the Horn uniformization of Kapranov-Huh. We characterize all choices of minimal kinematics on the moduli space $\mathcal{M}_{0,n}$. These choices are motivated by the CHY model in physics and they are represented combinatorially by 2-trees. We compute 2-tree amplitudes, and we explore extensions to non-planar on-shell diagrams, here identified with the hypertrees of Castravet-Tevelev.
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The CEGM NLSM
A systematic deformation theory for CEGM amplitudes yields generalized nonlinear sigma model amplitudes, with dimension gcd(k,n)-1 for pure deformations and an embedding of ordinary NLSM amplitudes as residues.