This Wednesday (30 October 2024) at 15:00 at B404, we have the Mathematics and Theoretical Physics Seminar by Mario García‐Fernández from el Instituto de Ciencias Matemáticas (Icmat) y la Universidad Autónoma de Madrid (UAM). In addition, at 14:00 at D450, Mario will also host a pre‐seminar talk intended to be accessible to MSc and beginning PhD students. After the seminar talk, there will be refreshments at the Connect Area on the 3rd floor of Spectra.
One of the major successes of string theory is its ability to derive general relativity: there is a field theory living on the 1-dimensional string (a 2d conformal field theory), whose consistency depends on it being a fixed point of a vector field called renormalisation group flow. In turn, the condition for being a fixed point of this flow turns out to precisely reproduce the Einstein field equations of general relativity in the simplest case. Not only is this flow (called Ricci flow) of immense physical interest, but it is also of great mathematical interest: it is a key ingredient in the proof of the Poincaré conjecture, one of the 7 Millenium Problems. Strings, however, come with a whole host of other fields required by supersymmetry, and hence we obtain many other variants of Ricci flow. Mario will discuss the flow coming from a version of string theory (called heterotic), and discuss its links to the famous conjecture (called Reid’s fantasy) that string theory, as a theory of quantum gravity, allows arbitrary topological changes consistent with supersymmetry (or, in mathematical terms, that the moduli spaces of certain Calabi–Yau manifolds — spaces on which strings can live — are all connected by certain topology-changing operations, called conifold transitions, which are allowed by string theory).
Title: Pluriclosed flow and the Hull–Strominger system
Abstract: I will overview joint work with Raúl González Molina and Jeffrey Streets in arXiv:2408.11674 about a natural extension of pluriclosed flow, where the evolution of the hermitian metric on the complex manifold X is further coupled to a hermitian metric on a holomorphic vector bundle V over X. Flow lines are special solutions of the generalized Ricci flow in generalized geometry, and hence of the renormalization group flow in the heterotic sigma model. Using this, we interpret the flow as a version of Donaldson’s Hermitian–Yang–Mills flow in the realm of higher gauge theory. We will comment on the higher regularity structure of the flow and on global existence and convergence results on special backgrounds. If time allows, we will also discuss the relationship to the Hull–Strominger system and, conjecturally, to the geometrization of Reid’s fantasy.