SU(3) 2 | VerlindeDB

\(\operatorname{SU}(3)_{2}\): \( A_{2} \) at level \(2\)

Fusion Ring

\[ \begin{array}{llllll} \htmlTitle{1\otimes 1}{1} & & & & & \\ \htmlTitle{2\otimes 1}{2} & \htmlTitle{2\otimes 2}{3} & & & & \\ \htmlTitle{3\otimes 1}{3} & \htmlTitle{3\otimes 2}{1} & \htmlTitle{3\otimes 3}{2} & & & \\ \htmlTitle{4\otimes 1}{4} & \htmlTitle{4\otimes 2}{6} & \htmlTitle{4\otimes 3}{5} & \htmlTitle{4\otimes 4}{5 \oplus 2} & & \\ \htmlTitle{5\otimes 1}{5} & \htmlTitle{5\otimes 2}{4} & \htmlTitle{5\otimes 3}{6} & \htmlTitle{5\otimes 4}{1 \oplus 6} & \htmlTitle{5\otimes 5}{4 \oplus 3} & \\ \htmlTitle{6\otimes 1}{6} & \htmlTitle{6\otimes 2}{5} & \htmlTitle{6\otimes 3}{4} & \htmlTitle{6\otimes 4}{4 \oplus 3} & \htmlTitle{6\otimes 5}{5 \oplus 2} & \htmlTitle{6\otimes 6}{1 \oplus 6} \\ \end{array} \]

Frobenius-Perron Dimensions

SimpleNumericSymbolic
\( 1\)\(1.000\)\( 1 \)
\( 2\)\(1.000\)\( 1 \)
\( 3\)\(1.000\)\( 1 \)
\( 4\)\(1.618\)\( \frac{1}{2} + \frac{\sqrt{5}}{2} \)
\( 5\)\(1.618\)\( \frac{1}{2} + \frac{\sqrt{5}}{2} \)
\( 6\)\(1.618\)\( \frac{1}{2} + \frac{\sqrt{5}}{2} \)
\( D^2\)10.854\(\frac{3 \sqrt{5}}{2} + \frac{15}{2}\)

Modular Data

Twist Factors

\[ \begin{pmatrix} \htmlTitle{\theta_{1}}{0} & \htmlTitle{\theta_{2}}{\frac{4}{3}} & \htmlTitle{\theta_{3}}{\frac{4}{3}} & \htmlTitle{\theta_{4}}{\frac{8}{15}} & \htmlTitle{\theta_{5}}{\frac{8}{15}} & \htmlTitle{\theta_{6}}{\frac{6}{5}} \end{pmatrix} \]

S Matrix

\[ \left(\begin{array}{llllll} \htmlTitle{S_{1; 1}}{1} & & & & & \\ \htmlTitle{S_{2; 1}}{1} & \htmlTitle{S_{2; 2}}{-\zeta_{60}^{10}} & & & & \\ \htmlTitle{S_{3; 1}}{1} & \htmlTitle{S_{3; 2}}{\zeta_{60}^{10} - 1} & \htmlTitle{S_{3; 3}}{-\zeta_{60}^{10}} & & & \\ \htmlTitle{S_{4; 1}}{-\zeta_{60}^{14} + \zeta_{60}^{6} + \zeta_{60}^{4}} & \htmlTitle{S_{4; 2}}{\zeta_{60}^{10} + \zeta_{60}^{8} - \zeta_{60}^{2} - 1} & \htmlTitle{S_{4; 3}}{\zeta_{60}^{14} - \zeta_{60}^{10} - \zeta_{60}^{8} - \zeta_{60}^{6} - \zeta_{60}^{4} + \zeta_{60}^{2} + 1} & \htmlTitle{S_{4; 4}}{\zeta_{60}^{10}} & & \\ \htmlTitle{S_{5; 1}}{-\zeta_{60}^{14} + \zeta_{60}^{6} + \zeta_{60}^{4}} & \htmlTitle{S_{5; 2}}{\zeta_{60}^{14} - \zeta_{60}^{10} - \zeta_{60}^{8} - \zeta_{60}^{6} - \zeta_{60}^{4} + \zeta_{60}^{2} + 1} & \htmlTitle{S_{5; 3}}{\zeta_{60}^{10} + \zeta_{60}^{8} - \zeta_{60}^{2} - 1} & \htmlTitle{S_{5; 4}}{-\zeta_{60}^{10} + 1} & \htmlTitle{S_{5; 5}}{\zeta_{60}^{10}} & \\ \htmlTitle{S_{6; 1}}{-\zeta_{60}^{14} + \zeta_{60}^{6} + \zeta_{60}^{4}} & \htmlTitle{S_{6; 2}}{-\zeta_{60}^{14} + \zeta_{60}^{6} + \zeta_{60}^{4}} & \htmlTitle{S_{6; 3}}{-\zeta_{60}^{14} + \zeta_{60}^{6} + \zeta_{60}^{4}} & \htmlTitle{S_{6; 4}}{-1} & \htmlTitle{S_{6; 5}}{-1} & \htmlTitle{S_{6; 6}}{-1}\end{array}\right) \]

Central Charge

\[c = \frac{16}{5} \]