Abstract :
The explicit (all-order in fermions) form of the kappa-symmetric D3-brane probe action was previously found in the two maximally supersymmetric type IIB vacua: flat space and AdS5×S5. Here we present the form of the action in the third maximally supersymmetric type IIB background: gravitational plane wave supported by constant null 5-form strength. We study D3-brane action in both covariant and light cone kappa symmetry gauges. Like the fundamental string action, the D3-brane action takes a simple form once written in the light cone kappa-symmetry gauge. We also consider the N=4 SYM theory in 4d plane wave background. Since some (super)symmetries of plane wave SYM action are friendly to (super)symmetries of the type IIB superstring in plane wave Ramond–Ramond background we suggest this SYM model may be useful in the context of AdS/CFT duality. We develop the Hamiltonian light cone gauge formulation for this theory.
