N=1/2 Super Yang-Mills Theory on Euclidean AdS2xS2
  We study D-branes in the background of Euclidean AdS2xS2 with a graviphoton field turned on. As the background is not Ricci flat, the graviphoton field must have both self-dual and antiself-dual parts. This, in general, will break all the supersymmetries on the brane. However, we show that there exists a limit for which one can restore half of the supersymmetries. Further, we show that in this limit, the N=1/2 SYM Lagrangian on flat space can be lifted on to the Euclidean AdS2xS2 preserving the same amount of supersymmetries as in the flat case. We observe that without the C-dependent terms present in the action this lift is not possible. 
Ali Imaanpur, Shahrokh Parvizi