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Conformal dimension of a scalar function?

  1. Sep 14, 2008 #1
    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].
    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.
  2. jcsd
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