BenTheMan
Mar17-07, 11:29 PM
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
S=\frac{1}{4g}\int d^Dx \sqrt{g}Tr\left(F_{\mu\nu}F^{\mu \nu})
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):
T^{\alpha\beta} = g^{\alpha\beta}F_{\mu\nu}F^{\mu \nu}.
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):
\partial_{\alpha}T^{\alpha\beta} = \partial^{\beta}F_{\mu\nu}F^{\mu \nu}.
Can anyone point me in the right directions? Am I missing something in the actoin (i.e. a hiding metric)?
S=\frac{1}{4g}\int d^Dx \sqrt{g}Tr\left(F_{\mu\nu}F^{\mu \nu})
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):
T^{\alpha\beta} = g^{\alpha\beta}F_{\mu\nu}F^{\mu \nu}.
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):
\partial_{\alpha}T^{\alpha\beta} = \partial^{\beta}F_{\mu\nu}F^{\mu \nu}.
Can anyone point me in the right directions? Am I missing something in the actoin (i.e. a hiding metric)?