# Einstein-Yang-Mills question

1. Dec 4, 2006

### coalquay404

I'm away from my computer (and, unfortunately, my passwords for online journal access) and I'm having a moment of forgetfulness. Can somebody confirm for me that the Einstein-Yang-Mills action with cosmological constant is the following?

$$S = \int d^5x \sqrt{|g^{(5)}|}\left(\frac{1}{16\pi G_{(5)}}(R-2\Lambda_{(5)}) - \frac{1}{4\overline{e}^2}F^{a}_{IJ}F^{aIJ}\right),$$

where

$$F^a_{IJ} = \partial_IA^a_J - \partial_JA^a_I + \epsilon_{abc}A^b_IA^c_J$$

and $G$ and $\overline{e}$ are, respectively, Newton's constant and the coupling constant of the gauge field theory? Thanks.

Last edited: Dec 4, 2006