SU(2) 4 | VerlindeDB

\(\operatorname{SU}(2)_{4}\): \( A_{1} \) at level \(4\)

Fusion Ring

\[ \begin{array}{lllll} \htmlTitle{1\otimes 1}{1} & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{1} & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{4} & \htmlTitle{3\otimes 3}{1 \oplus 5} & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{3} & \htmlTitle{4\otimes 3}{5 \oplus 2} & \htmlTitle{4\otimes 4}{1 \oplus 5} & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{5} & \htmlTitle{5\otimes 3}{3 \oplus 4} & \htmlTitle{5\otimes 4}{3 \oplus 4} & \htmlTitle{5\otimes 5}{1 \oplus 5 \oplus 2} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(1.732\)\( \sqrt{3} \)
\( 4\)\(1.732\)\( \sqrt{3} \)
\( 5\)\(2.000\)\( 2 \)
\( D^2\)12.000\(12\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{0} & \htmlTitle{\theta_{3}}{\frac{1}{4}} & \htmlTitle{\theta_{4}}{\frac{5}{4}} & \htmlTitle{\theta_{5}}{\frac{2}{3}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{lllll} \htmlTitle{S_{1; 1}}{1} & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{1} & & & \\ \htmlTitle{S_{3; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4}} & \htmlTitle{S_{3; 2}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4}} & \htmlTitle{S_{3; 3}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4}} & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4}} & \htmlTitle{S_{4; 2}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4}} & \htmlTitle{S_{4; 3}}{\zeta_{48}^{12} - 2 \zeta_{48}^{4}} & \htmlTitle{S_{4; 4}}{-\zeta_{48}^{12} + 2 \zeta_{48}^{4}} & \\ \htmlTitle{S_{5; 1}}{2} & \htmlTitle{S_{5; 2}}{2} & \htmlTitle{S_{5; 3}}{0} & \htmlTitle{S_{5; 4}}{0} & \htmlTitle{S_{5; 5}}{-2}\end{array}\right) \]

Central Charge

\[c = 2 \]