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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
expanded at Chan-Paton bundle the Idea-section and added two pointers to lecture notes. Also expanded at Freed-Witten anomaly a little.
I’m not sure I understand how to derive the transformation $A\mapsto A+a, B\mapsto B+d a$, is it supposed to be an automorphism of $Fields$, hence a natural transformation in the arrow category?
I have re-typeset the diagram in tikz
, to make it clearer: here.
In words: the field content is a twisted unitary connection modeled by a map in the slice over $\mathbf{B}^2 U(1)_{conn}$ into $\mathbf{Fields}$, with the domain encoding the twist(ing gerbe), and so acting on this by automorphisms of the twist means to pre-compose this slice-map by an automorphism of the domain, which, if we fix the actual domain space $X$, is just a gauge-transformation of the gerbe connection, locally by some 1-form $\alpha$.
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