I attempted to edit the question wrapping M5-branes on a Riemann surface so that it reads as follows:

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AdS/CFT gives us a way to use geometry to study field theory! I am trying to wrap M5-branes on a Riemann surface $\Sigma_{g}$. In my problem, for a Riemann surface in 11d, the normal bundle is max $SO(5)$. Here is my question: How do we put $SO(2)$ in $SO(5)$?

Urs Schreiber suggests the following mathematically precise interpretation of the question, which probably addresses the concerns of those who commented or who had voted to put the OP on hold:

There is a famous construction of (N=2)-supersymmetric 4-dimensional Yang-Mills field theories and their Seiberg-Witten theory from the N=(2,0)-superconformal 6-dimensional field theory on the worldvolume of M5-branes: by Kaluza-Klein-compactifying the latter on a Riemann surface. This construction was revived more recently in 2009 by the influential article

- Davide Gaiotto, N=2 dualities (arXiv:0904.2715)
On page 22 of this article, around the displayed formula (2.27), the author mentions that the Kaluza-Klein compactification of the 6d theory on a Riemann surface involves a “well known twisting procedure” of the holonomy of the Riemann surface by choosing an SO(2)-subgroup of the SO(5) group that is the “R-symmetry” group of the 6-dimensional supersymmetric field theory (the group under which its supercharges transform).

Question:What is this “well known twisting procedure” exactly, and how does it work? Of course I know how to find $SO(2)$-subgroups of $SO(5)$, but what does such a choice amount to in the context of the construction of an N=2, D=4 SYM from the 6d-field theory on the 5-brane? Where is this twisting procedure discussed in the literature?

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For some reason, when I try to save the edits, it keeps telling me the desired link is not allowed. Can someone explain what's going on?

`arXiv:`

as a url protocol, which is wrong. It might have been whining about having a link with a url name which is different from the linked url. If these were actual urls this kind of deception shouldn't be allowed, but in this case the link name is not actually an url, it's an arXiv identifier. $\endgroup$ – François G. Dorais♦ Jun 28 '13 at 23:52