Operadic renormalisation group

Bruno Vallette (Sorbonne U, Paris)

Oct 12. 2020, 13:15 — 14:00

The operadic interpretation of the Batalin--Vilkovisky formalism given by Mnev and Merkulov opened the doors to the operadic calculus in renormalisation theory. These authors showed that the passage from an action to an effective action is nothing but the application of the homotopy transfer theorem of unimodular Lie bialgebras, which is a structure encoded by a wheeled properad. In some sense, this is not a surprise since the homotopy transfer theorem relies on some homological perturbation method. Dotsenko--Shadrin--Vallette proved that the homotopy transfer theorem can be obtained by the action of seminal elements of the deformation group obtained by integrating operadic convolution pre-Lie algberas. In this talk, I will explain how to integrate, with graph exponentials, properadic convolution algbras which encode the deformation theory of types of bialgebras. The action of some seminal elements of this new deformation group gives the homotopy transfer theorem for these types of bialgebras, so this new group of symmetries is a universal renormalisation group. This is a joint work with Ricardo Campos. 



Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Higher Structures Emerging from Renormalisation - partially postponed (Online Workshop)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)