• mathematical physics
• higher-form symmetries
• generalized global symmetries
• framing
• QFT
• topological defects

In this thesis we study the possible framing dependence of topological defects, of general dimension and in general dimension, in a Quantum Field Theory.
We start by a review of higher-form symmetries, focusing on their description in terms of topological defects, on the notion of background gauge fields and on possible anomalies in the case of a discrete gauge group.
We then review the origin of framing dependence in the motivating example of Chern-Simons theory and give an interpretation in terms of homotopy classes of sections of the normal bundle. We then generalize this interpretation to propose a classification of possible local framing dependences in higher dimensions in terms of the Pontrjagin duals of homotopy groups of Stiefel manifolds.
Finally, we proceed to examine some examples in discrete gauge theories, relating the results to the previous classification.