1:30 pm MCP 201
A Geometric Formulation of the Cosmological Wavefunction.
Is there a geometric object underlying the cosmological wavefunction for Tr ϕ3 theory, just as associahedra underlie scattering amplitudes? In this talk, I will describe a new class of polytopes - Cosmohedra - that answer this question. I will start by reviewing the perturbative computation of the wavefunction and explain how it is organized in terms of collections of non-overlapping subpolygons living inside the momentum polygon. This combinatorial information is much richer than that of Tr ϕ3 amplitudes, where the diagrams correspond to triangulations of the same polygon. Nonetheless, as I will show the geometric descriptions are closely related — the polytopes for cosmology are obtained by "blowing up" the faces of the associahedron in a natural way. I will give a concrete definition of this class of polytopes, show how they work in some simple examples, and describe a number of open questions about the physics and mathematics associated with them.
Is there a geometric object underlying the cosmological wavefunction for Tr ϕ3 theory, just as associahedra underlie scattering amplitudes? In this talk, I will describe a new class of polytopes - Cosmohedra - that answer this question. I will start by reviewing the perturbative computation of the wavefunction and explain how it is organized in terms of collections of non-overlapping subpolygons living inside the momentum polygon. This combinatorial information is much richer than that of Tr ϕ3 amplitudes, where the diagrams correspond to triangulations of the same polygon. Nonetheless, as I will show the geometric descriptions are closely related — the polytopes for cosmology are obtained by "blowing up" the faces of the associahedron in a natural way. I will give a concrete definition of this class of polytopes, show how they work in some simple examples, and describe a number of open questions about the physics and mathematics associated with them.
Event Type
Dec
4