2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/198048We construct the free field representation of the affine currents, energy-momentum tensor and screening currents of the first kind of the current superalgebra $gl(m|n)_k$ uniformly for $m=n$ and $m\neq n$. The energy-momentum tensor is given by a linear combination of two Sugawara tensors associated with the two independent quadratic Casimir elements of $gl(m|n)$.Latex file, 15 pagesHigh Energy Physics - TheoryMathematical Physicstext