Aspects of D-brane dynamics in supergravity backgrounds with fluxes, kappa-symmetry and equations of motion. Part IIB

We derive and carry out a detailed analysis of the equations of motion of the type IIB D-branes in generic supergravity backgrounds with fluxes making account of the worldvolume Born-Infeld gauge field and putting a special emphasis on the structure of the Dirac equation for Dp-brane fermionic modes. We present an explicit form of the worldvolume field equations for each of the Dp-branes (p=1,3,5,7,9) in the cases in which the Neveu-Schwarz flux and the Ramond-Ramond p-form flux along the Dp-brane worldvolume are zero and the supergravity backgrounds do not necessarily induce the worldvolume Born-Infeld flux. We then give several examples of D3-, D5- and D7-brane configurations in which the worldvolume Born-Infeld flux is intrinsically non-zero and therefore must be taken into account in studying problems where such branes are involved. The examples include D3- and D5-brane instantons carrying (self-dual) worldvolume gauge fields in warped compactification backgrounds.