Zamolodchikov's c-theorem

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

$$ c=-\int_{0}^{\infty}dr \frac{2\dot{C}}{r}=\int_{0}^{\infty}dr \frac{3\dot{H}}{2r}=\frac{3}{2}\int_{0}^{\infty}dr r^3\langle \Theta(z,\bar{z})\Theta(0,0) \rangle $$

encyclopedia

• http://en.wikipedia.org/wiki/C-theorem