The Tameness of Quantum Field Theory

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.

cosmology and nongalactic astrophysicsgeneral relativity and quantum cosmologyHEP - phenomenologyHEP - theorymathematical physics

Audience: researchers in the discipline

AnLy Strings and Fields online seminars