# How to count on-shell DoF of a gauge theory?

1. Apr 5, 2010

### ismaili

Suppose I have a gauge potential $$A_{\mu\nu}$$, which is totally antisymmetric, if, say, the theory is in 6 dimensions, so that there are $$6\times5/2 = 15$$ degrees of freedom.

For the action $$S = \int d^6x F_{\mu\nu\rho}F^{\mu\nu\rho}$$, where
$$F_{\mu\nu\rho}\equiv \partial_\mu A_{\nu\rho} + \partial_{\nu}A_{\rho\mu} + \partial_{\rho}A_{\mu\nu}$$, we would have the following equation of motion
$$\partial_\lambda F^{\mu\nu\lambda} = 0$$

The question is, how to count the on-shell degrees of freedom of the gauge potential? or, before solving the equations of motion, how to know the number of independent equations?
Naively the number would be 15, but it turns out to be 9.

Is there any ideas? Thanks in advance.

Sincerely