Looking for structure in the cobordism conjecture

Abstract

The cobordism conjecture of the swampland program states that the bordism group of quantum gravity must be trivial. We investigate this statement in several directions, on both the mathematical and physical side. We consider the Whitehead tower construction as a possible organising principle for the topological structures entering the formulation of the conjecture. We discuss why and how to include geometric structures in bordism groups, such as higher U(1)-bundles with connection. The inclusion of magnetic defects is also addressed in some detail. We further elaborate on how the conjecture could predict Kaluza-Klein monopoles, and we study the gravity decoupling limit in the cobordism conjecture, with a few observations on NSNS string backgrounds. We end with comments in relation to T-duality, as well as the finiteness conjecture.

Open-closed correspondence of K-theory and cobordism

“…Hence, it is a relict of trying to narrow down the QG-structure following a bottom-up approach. Clearly, it would be very interesting to develop means to compute such refined gauge cobordism classes from first principles (see also [46]).…”

Dynamical Cobordism and the beginning of time: supercritical strings and tachyon condensation

“…The cobordism conjecture has been exploited at the topological level with interesting results, see e.g. [6,[10][11][12][13][14][15]. On the other hand, there is substantial progress in understanding the implications of the cobordism conjecture at the dynamical level.…”

Using Infographics for Improving Statistical Thinking Ability

“…This conjecture is closely connected to an old idea that the global symmetry is broken by quantum gravity [43]. For an illustration, we may consider the compact ball made of the black hole interior, which can smoothly evolve into the nothing according to the cobordism conjecture [42]. This is nothing more than the complete evaporation of the black hole, in which the global symmetry is not conserved since otherwise information is lost.…”

“…Recently, the bubble of nothing has drawn attention (see, for example, [33,34,35,36,37,38,39,40]) in the context of the swampland program. For instance, the cobordism conjecture [41] (see [42] for a review) argues that the compact space consistent with quantum gravity can shrink to zero size without any topological obstruction. This conjecture is closely connected to an old idea that the global symmetry is broken by quantum gravity [43].…”