Stueckelberg fields and the global degree of freedom of Unimodular Gravity

In this talk, we will analyze how the global degree of freedom that is present in Unimodular Gravity (but not in General Relativity) materializes in the Stueckelberg procedure. The idea is to apply the latter to General Relativity and Unimodular Gravity in order to get a new theory with an enhanced symmetry containing them both. In this setting, we realize that Stueckelberg-ing one of them and then gauge fixing to the other one is not consistent. Such restriction cannot be achieved with a legal gauge fixing, due to the discontinuity in the number of global degrees of freedom.