Lectures on Conformal Field Theory

Abstract

These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions, with applications related to topics of particular interest: topics include the conformal bootstrap program, boundary conformal field theory, and applications related to the AdS/CFT correspondence. We assume the reader to be familiar with quantum mechanics at the graduate level and to have some basic knowledge of quantum field theory. Familiarity with string theory is not a prerequisite for this lectures, although it can only help.

Figures (17)

• Figure 1: This image illustrates how rescaling distances preserves the angle $\Delta\theta$, even when we have rescaled $r_1\rightarrow r_2$ and $s_1\rightarrow s_2$.
• Figure 2: The phase diagram for the ferromagnetic/paramagnetic phase transition. Above the solid line, $M>0$ and below it, $M<0$. A conformal field theory lives at $T_c$.
• Figure 3: A simplified phase diagram for water. The critical point is marked.
• Figure 4: Example of RG flow in the space of two couplings. The point $g_*$ is a fixed point, and both stable and unstable flows are visible. The direction of arrows represents the flow from high energies to low energies.
• Figure 5: Sum of contour integral corresponding to the contour used in the text.