Properties of branes in curved spacetimes

A generic property of curved manifolds is the existence of focal points. Weshow that branes located at focal points of the geometry satisfy specialproperties. Examples of backgrounds to which our discussion applies are AdS_m xS^n and plane wave backgrounds. As an example, we show that a pair of AdS_2branes located at the north and south pole of the S^5 in AdS_5 x S^5 are halfsupersymmetric and that they are dual to a two-monopole solution of N=4 SU(N)SYM theory. Our second example involves spacelike branes in the (Lorentzian)plane wave. We develop a modified lightcone gauge for the open string channel,analyze in detail the cylinder diagram and establish open-closed duality. Whenthe branes are located at focal points of the geometry the amplitude acquiresmost of the characteristics of flat space amplitudes. In the open stringchannel the special properties are due to stringy modes that become massless.Comment: 41 pages; v2:typos corrected, ref adde