  In this work the pure spinor formulation of the superstring is used to study
quantum corrections to the left current OPE algebra of the coset $PSU(2,
2|4)/SO(4, 1) \times SO(5)$ sigma model, which describes the superstring
dynamics in the $AdS_5 \times S^5$ background. In particular, the one loop
corrections to the simple poles of the bosonic currents are computed. Unlike
the case of the double poles, we show that the simple poles suffer corrections,
which are important since the simple poles contribute to the four point
amplitudes. We show that the only contribution to the simple poles comes from
the pure spinor Lorentz currents.
