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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeSep 5th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexexpanded at _[[Chan-Paton bundle]]_ the Idea-section and added two pointers to lecture notes. Also expanded at _[[Freed-Witten anomaly]]_ a little.

   expanded at Chan-Paton bundle the Idea-section and added two pointers to lecture notes. Also expanded at Freed-Witten anomaly a little.

2. • CommentRowNumber2.
   • CommentAuthorperezl.alonso
   • CommentTimeJul 3rd 2024
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   Author: perezl.alonso
   Format: MarkdownItexI'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’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?

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeJul 3rd 2024
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have re-typeset the diagram in `tikz`, to make it clearer: [here](https://ncatlab.org/nlab/show/Chan-Paton+bundle#TransformationsOfBackgroundBField). 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 $\alpha$. <a href="https://ncatlab.org/nlab/revision/diff/Chan-Paton+bundle/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/Chan-Paton+bundle/9">v9</a>, <a href="https://ncatlab.org/nlab/show/Chan-Paton+bundle">current</a>

   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 $\alpha$.

   diff, v9, current