IAS Special High Energy Theory Seminar

The Institute for Advanced Study requires that all adult visitors, collaborators, conference and on-campus seminar attendees and outside vendors coming to the Institute are required to have completed a COVID-19 vaccination and booster in order to enter the IAS campus. Individuals must be prepared to present proof of vaccination if asked and are expected to follow the Institute's Covid-19 Procedures. Masks are optional while indoors. Additional information can be found at:
https://www.ias.edu/covid-19-procedures

This seminar will be presented in-person and on Zoom.
https://theias.zoom.us/j/84116605050?pwd=VHV6VkRUM3hkM2dFSlo2QWJiUWtPdz09

Abstract: In this talk we introduce a generalized notion of finiteness and argue that it common to many quantum field theories. The underlying mathematical foundation lies in tame geometry, which is built from o-minimal structures introduced in mathematical logic. We give a brief introduction to this fascinating mathematical subject and formalize the connection between quantum field theories and logical structures. For renormalizable quantum field theories, we show that amplitudes at each order in the loop expansion are tame functions. We then discuss exact non-perturbative results and show that they are tame but only given constraints on the UV definition of the theory. We quantify our expectations on the tameness of conformal field theories and effective theories that can be coupled to quantum gravity. In particular, we present tameness conjectures about conformal field theory observables and propose universal constraints that render spaces of conformal field theories to be tame sets.