Yang Mills Stress Tensor

  • Thread starter BenTheMan
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  • #1
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Main Question or Discussion Point

I am working through a set of notes on conformal field theory by Schellekens and want to show the conformal invariance of N=4 SYM theory in four dimensions. I start with the action
[tex]S=\frac{1}{4g}\int d^Dx \sqrt{g}Tr\left(F_{\mu\nu}F^{\mu \nu})[/tex]
There's only the metric in the action to worry about, in the Jacobian. (Is this wrong?)

But then the stress tensor I get is this (Abelian case):
[tex]T^{\alpha\beta} = g^{\alpha\beta}F_{\mu\nu}F^{\mu \nu}[/tex].

I'm pretty sure that this isn't right because I was assuming I'd use the SYM equation of motion to show the divergence condition on the stress tensor. Instead, I get something like (Abelian case):
[tex]\partial_{\alpha}T^{\alpha\beta} = \partial^{\beta}F_{\mu\nu}F^{\mu \nu}[/tex].

Can anyone point me in the right directions? Am I missing something in the actoin (i.e. a hiding metric)?
 
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Answers and Replies

  • #2
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[tex]
F^{\mu \nu} = g^{\mu \rho} g^{\nu \sigma} F_{\rho \sigma}
[/tex]
 
  • #3
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Sigh. Then I definitely see how to use the eom to get the divergence condition.

Thanks!
 

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