A free field representation of the gl(1|1)k current algebra at arbitrary level k is given in terms of two scalar fields and a symplectic fermion. The primary fields for all representations are explicitly constructed using the twist and logarithmic fields in the symplectic fermion sector. A closed operator algebra is described at integer level k. Using a new super spincharge separation involving gl(1|1)N and su(N)0, we describe how the gl(1|1)N current algebra can describe a non-trivial critical point of disordered Dirac fermions. Local gl(1|1) invariant lagrangians are defined which generalize the Liouville and sine-Gordon theories. We apply these new tools to the spin quantum Hall transition and show that it can be described as a logarithmic perturbation of the osp(2|2)k current algebra at k = −2.
"The gl(1|1) super-current algebra: the rôle of twist and logarithmic fields." Adv. Theor. Math. Phys. 13 (1) 259 - 291, January 2009.