We investigate the sky distribution of z \sim 6 Lyman break galaxies selected as i ^ { \prime } -dropouts having i ^ { \prime } - z ^ { \prime } > 1.45 down to z ^ { \prime } \leq 26.5 in the Subaru Deep Field ( SDF ) .
We discover 37 i ^ { \prime } -dropouts clustered in a projected comoving 21.6 \times 21.6 Mpc ^ { 2 } region at z = 6 , showing a local density excess .
Carrying out follow-up spectroscopy , we identify four of them as Ly \alpha emitters at z = 5.92 , 6.01 , 6.03 and 6.03 ( spread over a distance of 46.6 Mpc ) .
The number density of the cluster itself in SDF is \sim 2.2 \times 10 ^ { -7 } Mpc ^ { -3 } , smaller than those of protoclusters ( i.e. , forming galaxy clusters ) at z \sim 2 –5.7 .
Also , the structure shows \sim 4 –21 times larger galaxy number density than those of z \sim 6 galaxies in a general field .
It has a mass of M \sim 1.5 ^ { +1.8 } _ { -0.5 } \times 10 ^ { 15 } M _ { \odot } , comparable to those of z \sim 0 –5 protoclusters .
Since the contamination of our sample by interlopers is estimated to be quite low , 5.9 % , most of the other unconfirmed i ^ { \prime } -dropouts in the overdense region can be also z \simeq 6 galaxies .
Hence , it could be a candidate forming cluster at z \simeq 6 , representing a progenitor of galaxy clusters seen in the recent-day Universe .