Associahedrons and Stringy Canonical Forms

We construct the kinematic associahedron motivated by quantum field theory. We then construct a compactification for \(M_{0,n}^{+}\) motivated by string theory and realize it as a curvy associahedron (worldsheet associahedron) and a positive geometry. Finally, we introduce stringy integrals, which on some limit determines the kinematic associahedron and its canonical function, and on another limit gives a diffeomorphism between the interior of the kinematic associahedron and the worldsheet associahedron, thus relating their canonical functions and canonical forms.

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Date published: Wednesday, November 15, 2023