Conformal Field Theory

Course description

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 correlation 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 ideally have taken QFT I and ACTP. Please register to the course on the CTS/KSL.

Lecturer

Prof. Dr. Susanne Reffert

Literature

• Philippe Di Francesco et al., Conformal Field Theory (Springer) - main source
• Slava Rychkov, EPFL Lectures on Conformal Field Theory in D>=3 Dimensions (Springer) - source for some d>2 topics not treated in Di Francesco
• Joshua Qualls, Lectures on Conformal Field Theory, arXiv:1511.04074 - based largely on the above two (some errors remain in this text)
• Paul Ginsparg, Applied Conformal Field Theory, arXiv:hep-th/9108028 - mostly 2d, very well done
• David Tong, Lectures on String Theory, Chapter 4, https://www.damtp.cam.ac.uk/user/tong/string/four.pdf - 2d only, introduces all important concepts from a slightly different angle
• Hugh Osborn, Lectures on Conformal Field Theories in more than two dimensions, https://www.damtp.cam.ac.uk/user/ho/CFTNotes.pdf - very formal treatment
• Sidney Coleman, Aspects of Symmetry (Cambridge University Press) - Chapter 3 - I used part of this in the introduction
• David Simmons-Duffin, TASI Lectures on the Conformal Bootstrap, arXiv:1602.07982 - alternative treatment