The gl(1|1) super-current algebra: the role of twist and logarithmic fields

Understand

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 spin charge 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.