Nonanticommutative deformation of Script N = 4 SYM theory: the Myers effect and vacuum states

We propose a deformation of ${\cal N}=4$ SYM theoery induced bynonanticommutative star product. The deformation introduces new bosonic termswhich we identify with the corresponding Myers terms of a stack of D3-branes inthe presence of a five-form RR flux. We take this as an indication that thedeformed lagrangian describes D3-branes in such a background. The vacuum statesof the theory are also examined. In a specific case where the U(1) part of thegauge field is nonvanishing the (anti)holomorphic transverse coordinates of thebrane sit on a fuzzy two sphere. For a supersymmetric vacuum theantiholomorphic coordinates must necessarily commute. However, we alsoencounter non-supersymmetric vacua for which the antiholomorphic coordinates donot commute.Comment: 14 pages, minor changes, refs. adde