Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

i'm studying Conformal Field Theory using the big yellow book by Senechal et al. So far everything has been a smooth ride. I'm a bit stuck at the point where they derive the 2- and 3-point correlator for spinless fields.

Based on invariance under rotations and translations the correlator should depend only on the relative coords of the quasi primary fields and moreover - because of scaling invariance - this dependence should be of the type

[tex] f(|x_1-x_2|)\sim \lambda^{\Delta_1+\Delta_2}f(\lambda|x_1-x_2|)[/tex] where λ is the scaling and Δ the conformal weight.

But then those guys say that this is nothing but

[tex]\langle \phi(x_1)\phi(x_2)\rangle \sim \frac{1}{|x_1-x_2|^{\Delta_1+\Delta_2}} [/tex]

which is cannot follow. How do they know that the dependence is in the denominator and where does the exponent come from explicitely?

Any help is appreciated!

Thanks,

earth2

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# 2Point Correlator in CFTs

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