I attempted to edit the question http://mathoverflow.net/questions/134988/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 $SO(5)$?  

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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 (<b>want to insert arXiv link here</b>) 
  
> 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).
  
> <b>Question:</b> 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?