On the non-existence of totally localised intersections of D3/D5 branes in type IIB SUGRA

In the present paper we study the most general configuration of intersecting D3/D5 branes in type IIB supergravity satisfying Poincare invariance in the directions common to the branes and SO(3) symmetry in the totally perpendicular directions. The form of these configurations is greatly restricted by the Killing spinor equations and the equations of motion, which among other things, force the Ramond-Ramond scalar to be zero and do not permit the existence of totally localised intersections of this kind.