27 mar 2024 -- 14:30
Aula Tricerri, DIMaI, Firenze
Seminario di Geometria del Dini
Abstract.
Exotic spheres are seven-dimensional, compact manifolds, which have been shown (through a non-constructive existence theorem) to admit numerous Sasaki-Einstein metrics. For this reason, they are interesting candidates for various applications in string theory (specifically, within compactifications of M-theory), but have never been considered in this context due to the lack of a suitable description. In this talk, I will discuss metrics on exotic spheres viewed as non-principal S3 bundles over S4, i.e. Milnor's bundles, and summarise the findings presented in arXiv:2309.01703 (J. High Energ. Phys. 2023, 100 for the published version). I will outline the properties of these manifolds, mention the appearance of exotic differentiable structures in physics so far, and describe the potential application within the realm of string theory. All the necessary concepts will be introduced, and no prior knowledge on string theory will be required. Finally, I will present in detail an explicit metric for one of the exotic spheres, and comment on how this result might be applied in the compactification mechanism. I will end by discussing some open questions and interesting extensions of this work.