Chern-Simons Modular Data

Compute the modular data of Chern-Simons theories with compact connected gauge groups using the procedure in “A matrix S for all simple current extensions”. First, select an abelian, simply connected, or classical gauge group, then condense to quotient this by subgroups of its center.

Numerical: parent rank 2,500. Exact: parent rank 1,024 and condensate rank 256.

Step 1

Torus and Affine Lie Theory

Pointed Factor

Abelian GroupQuadratic Form

Affine Lie

Select a pointed (abelian) factor, represented equivalently by a metric group or a $\mathrm U(1)$ theory, a simply connected gauge group as a product of affine Lie categories, or both. Enter matrices by rows separated by semicolons. Tab to complete. In addition to simply connected groups, $\mathrm{PSU}(n)_k$ is available when $n\mid k$ ( $n$ odd), $2n\mid k$ or $k\equiv n\pmod{2n}$ ( $n$ even), or $\gcd(n,k)=1$ . $\mathrm{PSp}(2n)_k$ is available for $n,k\geq1$ ; $\mathrm{SO}(n)_k$ and $\mathrm{PSO}(n)_k$ for $n\geq3,\ k\geq1$ .