S-Duality and Categorical Gauge Theory

In this work, we revisit abelian S-duality in the context of higher gauge theory. By using a specific crossed module a set of transformations arise, which are known as the "thin" and "fat" transformations. The "fat" transformations are the ones introduced by hand to construct the S-dual theory. By utilizing crossed modules and higher gauge theory, we arrive at transformations referred to by some as "third-type transformations", giving these transformations a geometric interpretation, as transformations of a local 2-connection in a 2-principal bundle. This approach opens a new perspective to understand S-duality in non-abelian gauge theories through higher gauge theory.