2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/190712We construct plane wave backgrounds with time-dependent profiles corresponding to Penrose limits of NS5-branes with transverse space symmetry group broken from SO(4) to SO(2)\times Z_N. We identify the corresponding exact theory as the five-dimensional Logarithmic Conformal Field Theory (CFT) arising from the contraction of the SU(2)_{N'}/U(1)\times SL(2,R)_{-N} exact CFT, times R^5. We study several general aspects and construct the free field representation in this theory. String propagation and spectra are also considered and explicitly solved in the light-cone gauge.28 pages, LatexHigh Energy Physics - Theorytext