From the point of view of D-branes in the vicinity of the fixed points, the effective theory of the open strings attached to these D-branes is a supersymmetric field theory, whose space of vacua has a singular point, where additional massless degrees of freedom exist. The fields related with the closed string twisted sector couple to the open strings in such a way as to add a Fayet-Iliopoulos term to the supersymmetric field theory Lagrangian, so that when such a field acquires a non-zero vacuum expectation value, the Fayet-Iliopoulos term is non-zero, and thereby deforms the theory (i.e. changes it) so that the singularity no longer exists [http://www-spires.fnal.gov/spires/find/hep/www?j=NUPHA,B342,246.