Nonanticommutative deformation of N=4 SYM theory:: the Myers effect and vacuum states -: art. no. 017

We propose a deformation of 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.