"Non-unitary c(2,k+2) minimal models"의 두 판 사이의 차이

2012년 9월 15일 (토) 12:58 판

central charge
\(c(2,k+2)=1-\frac{3k^2}{k+2}\)
\(k \geq 3\), odd
primary fields have conformal dimensions
\(h_j=-\frac{j(k-j)}{2(k+2)}\), \(j\in \{0,1,\cdots,[k/2]\}\)
effective central charge
\(c_{eff}=\frac{k-1}{k+2}\)
dilogarithm identity
\(\sum_{i=1}^{[k/2]}L(\frac{\sin^2\frac{\pi}{k+2}}{\sin^2\frac{(i+1)\pi}{k+2}})=\frac{k-1}{k+2}\cdot \frac{\pi^2}{6}\)
character functions
\(\chi_j(\tau)=q^{h_j-c/24}\prod_{n\neq 0,\pm(j+1)}(1-q^n)^{-1}\)
to understand the factor \(q^{h-c/24}\), look at the finite size effect page also
quantum dimension and there recurrence relation
\(d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}\) satisfies
\(d_i^2=1+d_{i-1}d_{i+1}\) where \(d_0=1\), \(d_k=1\)

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 *  primary fields have conformal dimensions<br><math>h_j=-\frac{j(k-j)}{2(k+2)}</math>, <math>j\in \{0,1,\cdots,[k/2]\}</math><br>
 *  effective central charge<br><math>c_{eff}=\frac{k-1}{k+2}</math><br>
-*  dilogarithm identity<br><math>\sum_{i=1}^{[k/2]}L(\frac{\sin^2\frac{\pi}{k+2}}{\sin^2\frac{(i+1)\pi}{k+2}}})=\frac{k-1}{k+2}\cdot \frac{\pi^2}{6}</math><br>
+*  dilogarithm identity<br><math>\sum_{i=1}^{[k/2]}L(\frac{\sin^2\frac{\pi}{k+2}}{\sin^2\frac{(i+1)\pi}{k+2}})=\frac{k-1}{k+2}\cdot \frac{\pi^2}{6}</math><br>
 *  character functions<br><math>\chi_j(\tau)=q^{h_j-c/24}\prod_{n\neq 0,\pm(j+1)}(1-q^n)^{-1}</math><br>
 *  to understand the factor <math>q^{h-c/24}</math>, look at the [[finite size effect]] page also<br>
-*  quantum dimension and there recurrence relation<br><math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}}</math> satisfies<br><math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math><br>
+*  quantum dimension and there recurrence relation<br><math>d_i=\frac{\sin \frac{(i+1)\pi}{k+2}}{\sin \frac{\pi}{k+2}}</math> satisfies<br><math>d_i^2=1+d_{i-1}d_{i+1}</math> where <math>d_0=1</math>, <math>d_k=1</math><br>