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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)?

[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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