Discover the Basics of Conformal Field Theory: An Introduction for Beginners

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SUMMARY

Conformal Field Theory (CFT) is a specialized field theory characterized by a conformal symmetry group, which alters scales without changing angles. This symmetry differs from the Poincaré group and can be disrupted during the renormalization process, introducing a length scale and resulting in an anomaly. In two-dimensional CFT, the conformal group expands to an infinite dimensionality, presenting unique properties and challenges. For a deeper understanding, refer to "Conformal Field Theory" by Philippe Di Francesco et al., particularly chapter 4.

PREREQUISITES
  • Basic knowledge of quantum field theory
  • Understanding of symmetry groups, specifically the Poincaré group
  • Familiarity with the concept of renormalization in field theories
  • Knowledge of anomalies in quantum field theory
NEXT STEPS
  • Read "Conformal Field Theory" by Philippe Di Francesco et al., focusing on chapter 4
  • Explore the implications of anomalies in quantum field theory
  • Investigate the properties of infinite dimensional symmetry groups in two-dimensional CFT
  • Review Samalkhaiat's thread on conformal topics for additional insights
USEFUL FOR

This discussion is beneficial for theoretical physicists, quantum field theorists, and students seeking to understand the foundational concepts of Conformal Field Theory and its applications in modern physics.

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.
 

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