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We propose a deformation of ${\cal N}=4$ 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.
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