[AnLy] The Tameness of Quantum Field Theory

par Prof. Thomas Grimm (Utrecht University)

mercredi 22 févr. 2023, 16:00 → 17:00 Europe/Paris

Online seminar

 

Abstract: In this talk I will introduce a generalized notion of finiteness and argue that it appears in quantum field theories and in all well-understood string theory effective theories. The underlying mathematical foundation is described by the tame geometry that is built from o-minimal structures introduced in mathematical logic. For renormalizable quantum field theories, I will give a general proof that amplitudes at each order in the loop expansion are tame functions. I will discuss several exact non-perturbative results and show that they are tame but only given constraints on the UV definition of the theory. I will present new evidence that tameness is linked to a consistent coupling to quantum gravity. Motivated by these insights, I will suggest that sets of consistent physical theories and their observables can be used to define tame structures. I will make concrete conjectures how this is implemented for conformal field theories and comment on some of the implications.

Link: Zoom

AnLy: https://sites.google.com/view/anlystringsandfields