Among the general properties which every consistent quantum gravity theory in more than two dimensions is believed to satisfy is the absence of exact global symmetries: According to a by now well known conjecture, all symmetries in quantum gravity (in d > 2) are either gauged or ultimately broken. The absence of exact global symmetries has been reformulated more recently as the postulate that the cobordism group of quantum gravity should be trivial. Applied to compactifications of string theory, this conjecture predicts new types of (non-BPS) branes, whose role is to trivialize the cobordism group in the effective field theory.
In this ZMP seminar we will discuss the physics and mathematics around this circle of ideas. On the physics side we begin from a heuristic motivation of the no-global-symmetry conjecture from the point of view of black hole physics, we will review holographic arguments for it in the special case of quantum gravity in Anti-de Sitter spacetime.
On the mathematics side we describe global symmetries and their gauging from a categorical perspective, give a gentle introduction to cobordism groups and how to compute them, as well as their relation to invertible topological field theories.
We connect cobordism groups and quantum gravity theories and exemplify how the triviality of the cobordism group of quantum gravity requires the introduction of certain defects, leading to the prediction of new types of branes.
For questions about the seminar, or to get involved in any way, please contact Timo Weigand, Ingo Runkel or Julian Holstein.
The planned ZMP seminars and colloquia this semester are as follows: