Super spin-charge separation for class A, C and D disorder

We prove versions of super spin-charge separation for all three of the symmetry groups SU(N), Sp(2N) and SO( N) of disordered Dirac fermions in 2 + 1 dimensions, which involve the supercurrent algebras gl(1|1)(N), osp(2|2)(-2)N and osp(2|2)(N) respectively. For certain restricted classes of disordered potentials, the latter supercurrent algebra based conformal field theories can arise as non-trivial low energy fixed points. For all cases with such a fixed point, we compute the density of states exponents as a function of N.