What is conformal field theory?

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wam_mi
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Hi there,

Can anyone explain to me what Conformal Field Theory really is in brief summary? I do not mind if anyone wants to go into technical details as I have some basic knowledge of quantum field theory already.

Thank you
 

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I suggest you read "conformal field theory" by Philippe Di Francesco et al, chapter 4. :)

Conformal field theory is basically a field theory with a conformal symmetry group. This group can be seen as the group of all symmetries which only change scales, not angles. Ofcourse, this is another group then the Poincare group. However, as soon as you start to renormalize things this symmetry can be broken, because renormalization introduces a length scale; this is called an anomaly (a classical field theory which is broken as soon as you start to quantize things).

In two dimensions things become also interesting, because then the conformal group becomes infinite dimensional.