Theory HEP Seminar

Scattering Amplitudes from Intersection Theory

Sebastian Mizera

Perimeter Institute

Understanding of the rich geometry of moduli spaces of punctured Riemann surfaces can provide numerous insights into the computation of some physical observables, such as scattering amplitudes. Focusing on the genus-zero case, in this talk I will exemplify this interplay by introducing a generalization of the famous Riemann bilinear relations to string theory amplitudes. They give an identity between scattering amplitudes of open and closed strings, as well as auxiliary objects called intersection numbers of twisted cycles. If time permits, I will discuss a cohomological analogue of this construction, which allows to compute scattering amplitudes in various quantum field theories in two ways: either as residues around the boundaries of the moduli space, or as localization integrals on the support of the so-called scattering equations.