One approach to the Strong CP Problem (known as Nelson-Barr models) is to assume that parity is a gauge symmetry, which is spontaneously broken in the world around us. In this talk, we argue that the associated domain walls are exactly stable as the result of a topological gauge charge. We explain how these charges are compatible with the expected absence of global symmetries in quantum gravity as well as their relationship with the Swampland Cobordism Conjecture.

CalTech