Aspects of Scattering Amplitudes and Moduli Space Localization

Abstract

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Scattering equations in AdS: scalar correlators in arbitrary dimensions

“…The strategy in proving (4.12) will be to rewrite the integral localizing on solutions of scattering equations to that localizing on boundaries of M 0,n corresponding to the Riemann surface degenerating into trivalent diagrams. While in flat space case there are multiple ways of arriving at such a result, see, e.g., [47,[63][64][65], here we cannot use them reliably for operator-valued scattering equations. In other words, we do not have a reliable way of solving these constraints explicitly, or even predicting how many solutions they might have.…”

“…Making this statement more precise will require a computation of the appropriate integrands coming from spin-1 and 2 vertex operators, which will be given in a future publication. Finally, it might be interesting to construct a version of our AdS model in the context of sectorized/chiral string [95][96][97][98][99][100], together with its intersection theory interpretation [65], which introduces a non-trivial α dependence to double-copy.…”

On polytopes and generalizations of the KLT relations

“…Accompanying this line of work nearly simultaneously was the application of a novel class of mathematical objects known as twisted intersection numbers to the study of scattering amplitudes. Originally, the techniques of twisted intersection theory were used to study the KLT kernel in string theory [18], but have since been applied to general quantum field theories [19], Feynman integrals [20][21][22][23] and other aspects of scattering amplitudes, including recursion [24] and the double copy [25].…”

“…Indeed, the CHY formula is a special case of a twisted intersection number, in which the hyperplane arrangement yields the moduli space of marked Riemann spheres. For an extensive review of methods and formalism, the reader should consult [24]. One of the advantages of the method of twisted intersection numbers is the trivialization of identities such as the KLT relations, recasting them as statements of linear algebra.…”

“…Another very popular avatar of the double copy is due to Bern, Carrasco and Johansson (see [53][54][55][56] and references thereof and therein), in which the double copy is carried out at the level of individual Feynman diagrms, where kinematical and colour factors in the numerators obery identities that enable an essential 'squaring' of a gluon amplitude into a gravity amplitude. It has transpired of late that string amplitudes and intersection theory [24] may play a role in providing some insight into their origins. It may prove worthwhile to pursue this connection for theories with higher point interactions using the tools developed here.…”