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We consider a supersymmetric SU(4)$_c \times$SU(2)$_L \times$SU(2)$_R$ modelwith a minimal number of Higgs multiplets and Dirac and Majorana $CP$-violatingphases in the neutrino flavor mixing matrix. The model incorporates the chargedfermion masses and quark mixings, and uses type I seesaw to explain the solarand atmospheric neutrino oscillations. With the neutrino oscillation data oftwo mass squared differences and three flavor mixing angles, we employ thermalleptogenesis and the observed baryon asymmetry to find the allowed regions forthe Dirac and Majorana phases. For a normal neutrino mass hierarchy, we findthat the observed baryon asymmetry can be reproduced by a Dirac phase of around$\delta_{CP}=3 \pi/2$, which is strongly indicated by the recent T2K andNO$\nu$A data. For the case of inverted neutrino mass hierarchy, the predictedbaryon asymmetry is not compatible with the observed value.

Leptonic $CP$ Violation and Leptogenesis in Minimal Supersymmetric SU(4)$_c \times$SU(2)$_L \times$SU(2)$_R$