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(adsbygoogle = window.adsbygoogle || []).push({});

[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)?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Yang Mills Stress Tensor

**Physics Forums | Science Articles, Homework Help, Discussion**