Séminaire de Géométrie Tropicale
Mercredi 27 mars, 16h15 salle 1525-502
From strings to particles; on a tropical correspondence theorem in physics
Résumé :
String theory is a physics theory whose aim is to describe the world at scales much smaller than currently known. The reason why we don't see strings but particles is that those strings should be "too small" to be visible, and hence behave "effectively" as particles. We will show in a well defined and very precise case that the mathematical process by which the strings appear to be "too small" and behave "effectively" as if they were particles sweeping a one dimensional variety when propagating in space-time is actually well described by a tropical limit.
The essential part of this talk is hence devoted to the demonstration that a very common kind of integral appearing in string theory (known as "scattering amplitudes") over the moduli space of n-punctured Riemann spheres is mapped to an integral over the tropical moduli space of tropical graphs with n punctures in the limit where the length of the string goes to zero.