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, [tex]t^{++}{}_+[/tex], 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 [tex] z = \sigma^+ = \tau + i\sigma[/tex].(adsbygoogle = window.adsbygoogle || []).push({});

In other words, the conformal dimension is defined by the power of the transformation factor, for example,

[tex]t_+ \rightarrow \left(\frac{\partial z}{\partial\tilde{z}}\right)^1t_+[/tex]

hence, [tex]t_+[/tex] has conformal dimension 1.

However, I read from a text that the conformal dimension of [tex]\frac{1}{\sigma^+}[/tex] 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 [tex](\sigma^+ - \sigma'^+)^{-n}[/tex]??

Thanks in advance.

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

Dismiss Notice

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!

# Conformal dimension of a scalar function?

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

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