(Proposal ID) S14A-114 (PI) Shimakawa Rhythm (Proposal Title) Environmental Dependence in Physical States of Two Proto-Clusters at z>2 (Abstract) We propose to conduct a deep MOSFIRE spectroscopy of bright H emitters in the two densest proto-clusters ever known at z>2. The cluster membership of our targets are all confirmed with one or more emission lines identified by our previous MOIRCS spectroscopy (S13A-039). We now aim to go much deeper with the new spectrograph MOSFIRE on Keck which has a much greater sensitivity (>5~) compared to MOIRCS. With a multi-line diagnostics by detecting [OII], [OIII] and H emission lines for individual galaxies, and combining with existing or new H and [NII] information, we will fully quantify physical states of star-forming galaxies in the proto-clusters for the first time and investigate the environmental effects on galaxy formation: (1) True star formation rates (SFR) reliably corrected for dust extinction will unveil the nature of red H emitters, the key population under the influence of environmental effects. (2) Gaseous metallicities and ionization parameter will characterize the physical states of ISM in the formation phase of cluster early-type galaxies, (3) AGN activity in relation to star formation activity will scrutinize their co-activation and give clues to the origin of Maggorian relation in the cluster environment.