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

(begin edit)

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?

(end of edit)

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?

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

(begin edit)

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?

(end of edit)

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?

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

(begin edit)

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 (want to insert arXiv link here)

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?

(end of edit)

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?

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

(begin edit)

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?

(end of edit)

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?