# Conformal dimension of a scalar function?

1. Sep 14, 2008

### ismaili

Actually, I'm not fully understand what the meaning of conformal dimension is. But I know how to read off the conformal dimension of a tensor, say, $$t^{++}{}_+$$, then the conformal dimension is -2 + 1= -1, where the lower index carries conformal dimension 1 and upper index carries conformal dimension -1. The + index denotes the index for the light-cone coordinate $$z = \sigma^+ = \tau + i\sigma$$.
In other words, the conformal dimension is defined by the power of the transformation factor, for example,
$$t_+ \rightarrow \left(\frac{\partial z}{\partial\tilde{z}}\right)^1t_+$$
hence, $$t_+$$ has conformal dimension 1.
However, I read from a text that the conformal dimension of $$\frac{1}{\sigma^+}$$ is 1.
But I only know the definition of conformal dimension for tensors, how can I extend the definition of conformal dimension to the scalar function like $$(\sigma^+ - \sigma'^+)^{-n}$$??