Data di Pubblicazione:
2019
Citazione:
AMPLITUHEDRA FOR PHI^3 THEORY AT TREE AND LOOP LEVEL / G. Salvatori ; supervisor: D.KLEMM ; director of the school: M. Paris. Università degli Studi di Milano, 2019 Oct 25. 32. ciclo, Anno Accademico 2019. [10.13130/salvatori-giulio_phd2019-10-25].
Abstract:
In this thesis we explore a novel connection between scattering amplitudes and
positive geometries, which are semi-algebraic varieties iteratively defined by the
property of possessing a boundary structure which reduces into lower dimensional
version of themselves. The relevance of positive geometries in physics was first
discovered in the context of scattering amplitudes in N = 4 SYM and led to the
definition of the Amplituhedron. An analogue structure was very recently found to tie
tree level scattering amplitudes in the bi-adjoint scalar theory to the Stasheff
polytope and the moduli space of Riemann surfaces of genus zero. Here we further
extend this framework and show how the 1-loop integrand in bi-adjoint theory, or
more generally in a planar scalar cubic theory, is connected with moduli spaces of
more general Riemann surfaces. We propose hyperbolic geometry to be a natural
language to study the positive geometries living in various moduli spaces, then we
illustrate convex realizations of polytopes which are combinatorially equivalent to
them, but live directly in the kinematical space of amplitudes and integrands. Finally,
we show how to exploit these constructions to provide novel and efficient recursive
formulae for both tree level amplitudes and 1-loop integrands.
Tipologia IRIS:
Tesi di dottorato
Keywords:
Scattering Amplitudes; Amplituhedron; Quantum Field Theory
Elenco autori:
G. Salvatori
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