The Sliding Singlet Mechanism with Gauge Mediated Supersymmetry Breaking
  The sliding singlet mechanism is one of the most interesting solutions of the triplet-doublet splitting problem. We analyze this mechanism in the gauge mediated supersymmetry breaking scenario. We show that the sliding singlet mechanism does not work in the naive gauge mediation scenario because of the singlet linear terms derived from the gravity, although $F$ term is much smaller than the one in the gravity mediation scenario. We also consider the extension in order for the sliding singlet mechanism to work. 
Yuichi Chikira, Naoyuki Haba and Yukihiro Mimura