Aspects of Scattering Amplitudes and Moduli Space Localization
Abstract: We review a recent geometric formulation of the tree-level S-matrix of various quantum field theories, including gauge and gravity theories, in terms of intersection numbers of twisted cohomology groups on the moduli space of genus-zero curves with marked points. Scattering amplitudes are computed in terms of integrals over such moduli spaces that localize on worldsheets resembling Feynman diagrams and in certain circumstances coincide with the field-theory limit of string theory. We outline recursion relations that allow for explicit computations of S-matrices on the forgetful fibration of moduli spaces. We show that in the massless limit intersection numbers have another localization formula on the critical points of a certain Morse function.
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