Nucleosynthesis in core-collapse supernovae and GRB-metal-poor star connection

We review the nucleosynthesis yields of core-collapse supernovae (SNe) for various stellar masses, explosion energies, and metallicities. Comparison with the abundance patterns of metal-poor stars provides excellent opportunities to test the explosion models and their nucleosynthesis. We show that the abundance patterns of extremely metal-poor (EMP) stars, e.g., the excess of C, Co, Zn relative to Fe, are in better agreement with the yields of hyper-energetic explosions (Hypernovae, HNe) rather than normal supernovae. We note that the variation of the abundance patterns of EMP stars are related to the diversity of the Supernova-GRB connection. We summarize the diverse properties of (1) GRB-SNe, (2) Non-GRB HNe/SNe, (3) XRF-SN, and (4) Non-SN GRB. In particular, the Non-SN GRBs (dark hypernovae) have been predicted in order to explain the origin of C-rich EMP stars. We show that these variations and the connection can be modeled in a unified manner with the explosions induced by relativistic jets. Finally, we examine whether the most luminous supernova 2006gy can be consistently explained with the pair-instability supernova model.