2025 Summer: Global symmetries, cobordisms and quantum gravity

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.

Tom Banks, Nathan Seiberg: Symmetries and Strings in Field Theory and Gravity,
e-Print: 1011.5120 [hep-th]

Daniel Harlow, Hirosi Ooguri: Symmetries in Quantum Field Theory and Quantum
Gravity,
e-Print: 1810.05338 [hep-th]

John McNamara, Cumrun Vafa: Cobordism Classes and the Swampland,
e-Print: 1909.10355 [hep-th]

Arun Debbray, Markus Dierigl, Jonathan Heckman, Miguel Montero: Chronicles of
IIBordia: Dualities, Bordisms and the Swampland,
e-Print: 2302.00007 [hep-th]