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    CHY formulae in 4d

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    In this paper, we develop a rather general way to reduce integrands with polarization involved in the Cachazo-He-Yuan formulae, such as the reduced Pfaffian, its compactiffcation and its squeezing, as well as the new object for F^3 amplitude. We prove that the reduced Pfaffian vanishes unless evaluated on a certain set of solutions. It leads us to build up the 4d CHY formulae using spinors, which strains off many useless solutions. The supersymmetrization is straightforward and may provide a hint to understand ambitwistor string in 4d.Comment: typos fixe

    2m2m-Weak amenability of group algebras

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    A common fixed point property for semigroups is applied to show that the group algebra L1(G)L^1(G) of a locally compact group GG is 2m2m-weakly amenable for each integer m1m\geq 1.Comment: J. Math Anal. Appl. to appea