Tame geometry in QFTs and String Theory

Abstract: In this talk I will introduce a generalized notion of finiteness and argue that it appears in many well-understood string theory effective theories and in perturbative QFTs. The underlying mathematical foundation is described by the tame geometry that is built from o-minimal structures. I will briefly introduce this fascinating field of mathematics which is linking geometry and logic. I will then use some of the remarkable recent results from this field to discuss the tameness of (1) supergravity theories with N>=4, (2) flux compactifications of string theory, and (3) general n-loop QFT amplitudes. To frame these observations, I will propose a Tameness Conjecture that claims that consistent effective theories that can be coupled to gravity have to be tame.

HEP - theorymathematical physics

Audience: researchers in the topic

QFT and Geometry

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