Speaker
Description
In the mathematics of particle physics, it is not uncommon that a calculation should result in infinity. The longstanding hope has been that the correct theory of quantum gravity will act as a sort of universal UV regulator in the low-energy limit of QFT. As it stands, there is no one choice of regularisation that hints at any connection to quantum gravity, or which can be applied for all purposes and for all QFTs. String theory has certainly provided multiple insights in this regard, not least in terms of its natural exponential damping of UV divergences. Motivated by stringy behaviour in the UV, in this talk I will describe recent research that considers these questions. Beginning at the nexus of number theory and physics, I will discuss a general class of regulator functions based firstly on the work of Terence Tao. I will then show how the broad class of $\eta$-regulators that we define can be extended as a potentially generalised theory of regularisation (for all QFTs). After summarising a few important results in the extension to gauge theories, I will discuss the derivation of a master equation (in $\eta$ language) in which all symmetry preserving regularisation prescriptions must satisfy, before reviewing the extension of $\eta$-regularisation to n-loops. I will then conclude with a few comments on ongoing research that investigates how this generalised class of regulators relates to the UV finiteness of string theory.
