Abstract
We propose a deformation of 
= 4 SYM theory induced
by nonanticommutative star product. The deformation introduces new
bosonic terms which we identify with the corresponding Myers terms of
a stack of D3-branes in the presence of a five-form RR flux. We take
this as an indication that the deformed lagrangian describes D3-branes
in such a background. The vacuum states of the theory are also
examined. In a specific case where the U(1) part of the gauge field
is nonvanishing the (anti)holomorphic transverse coordinates of the
brane sit on a fuzzy two-sphere. For a supersymmetric vacuum the
antiholomorphic coordinates must necessarily commute. However, we also
encounter non-supersymmetric vacua for which the antiholomorphic
coordinates do not commute.