Zamolodchikov's c-theorem
imported>Pythagoras0님의 2013년 2월 25일 (월) 15:32 판
correlation functions
- $\langle T(z,\bar{z})T(0,0) \rangle =\frac{F(|z|^2)}{z^4}$
- $\langle \Theta(z,\bar{z})\Theta(0,0) \rangle =\frac{H(|z|^2)}{z^4}$
- $\langle T(z,\bar{z})\Theta(0,0) \rangle =\langle \Theta(z,\bar{z})T(0,0) \rangle \frac{G(|z|^2)}{z^3\bar{z}}$
C-function
- $C=2F-G-\frac{3}{8}H$
UV-limit
$$ c=-\int_{0}^{\infty}dr \frac{2\dot{C}}{r}=\int_{0}^{\infty}dr \frac{3\dot{H}}{2r}=\frac{3}{2}\int_{0}^{\infty}dr r^3\langle \Theta(z,\bar{z})\Theta(0,0) \rangle $$