Description
In this talk, I will present the recently developed mathematical framework of tameness as a candidate for a unifying finiteness principle underlying effective field theories. After introducing the central ideas of the formalism, I will show how it gives rise to a quantitative notion of complexity for EFTs, capturing the information required to specify a given theory. I will illustrate this perspective through explicit examples in which the complexity is finite, most notably in Seiberg-Witten theory. I will then formulate a conjecture according to which any EFT admitting a consistent ultraviolet completion in quantum gravity must exhibit finite complexity in this sense, and discuss the consequences of this idea for the swampland program.
