### Speaker

### Description

Theories with modular invariance are made finite by extreme UV/IR mixing. Finiteness then dictates that this must be the case even when supersymmetry is broken. Thus modular invariance gives us a way of thinking about the properties of non-supersymmetric strings without making any kind of assumptions about model building. In particular one can use number theoretical techniques (specifically the Rankin-Selberg-Zagier method) to extract an effective potential in terms of regulated supertraces – the equivalent of the Coleman-Weinberg potential. The understanding gained from this calculation allows us to inject several new ideas into ongoing discussions of the swampland. For example, we find that the distance conjecture can more appropriately be formulated in terms of these supertraces rather than distance scales. Using these results, we will see that there exist very general classes of modular invariant theories in which the distance conjecture holds as well as other classes in which it seems not to.