Conformal Field Theories (CFTs) are quantum field theories which are invariant under conformal transformations. They have a special status among QFTs are they appear in the fixed points of the renormalization group (RG) flow. They play a role in the description of critical phenomena in condensed matter physics, are related to quantum gravity via the AdS/CFT correspondence, and appear in the world-sheet description of string theory.
In this course, we will first study conformal transformations and the conformal group and then discuss the implications of conformal invariance for a QFT. We will study n-point functions in CFTs, representations of the conformal group, radial quantization and the state-operator correspondence. Since the conformal group has very different properties in two and higher dimensions, we will study these cases separately.
Towards the end of the semester, we will study some advanced topics.
In order to be able to follow this course, you should have taken QFT I and ACTP.