I am currently trying to go through some literature on the classification of symmetry protected topological phases. One shortcoming in my background is that I am unable to understand the physics-motivated discussions of gauge theory in the context of condensed matter physics. What is a background gauge field, emergent gauge fields etc. etc.?
I am looking for mathematically precise references that I can use to learn the relevant gauge theory (both with discrete and Lie groups) so I can better understand the literature.
Any help would be appreciated!