Matilda Delgado (Harvard) — Hamiltonian Cobordism

Matilda Delgado (Harvard)

I will discuss states charged under global symmetries detected by the Cobordism Conjecture in Quantum Gravity theories and examine when such states can be realized as smooth, finite-energy configurations in asymptotically flat spacetime. Assuming standard energy conditions on the stress-energy tensor, I will show that no such regular configurations exist when the relevant bordism generators fail to admit a metric of positive scalar curvature. For such symmetries, the charged states should therefore be singular, involve quantum matter that violates energy conditions or collapse the asymptotically flat spacetime. Such global symmetries are therefore not manifest in the IR. I will outline the implications of this for symmetries detected by spin bordism. Finally, I will consider the bordism groups of spin manifolds with positive scalar curvature and argue that they detect approximate global symmetries in the IR. Such symmetries are broken in the UV but from the low-energy perspective they signal the need to include energy condition-violating matter. Based on WIP with M. Montero and G. Tazzoli.