Trouble with space-like noncommutative field theory
  It is argued that the one-loop effective action for a space-like noncommutative scalar field theory does not exist. This indicates that such theories are not renormalizable already at one loop order and suggests supersymmetrization and reinvestigating other types of noncommutativity. 
V. Gayral, J.M. Gracia-Bondia, F. Ruiz Ruiz