ON THE BOUND-STATES OF P-BRANES AND (P-BRANES(2))

We study bound states of Dp-branes and D(p + 2)-branes. By switching o n a large magnetic field F on the (p + 2) brane, the problem is shown to admit a perturbative analysis in an expansion in inverse powers of F. It is found that, to the leading order in 1/F, the quartic potentia l of the tachyonic state from the open string stretched between the p- and (p + 2)-brane gives a vacuum energy which agrees with the predicti on of the BPS mass formula for the bound state. We generalize the disc ussion to the case of m p-branes plus 1 (p + 2)-brane with magnetic fi eld. The T-dual picture of this, namely several (p + 2)-branes carryin g some p-brane charges through magnetic Bur is also discussed, where t he perturbative treatment is available in the small F limit. We show t hat once again, in the same approximation, the tachyon condensates giv e rise to the correct BPS mass formula. The role of 't Hooft's toron c onfigurations in the extension of the above results beyond the quartic approximation as well as the issue of the unbroken gauge symmetries a re discussed. We comment on the connection between the present bound s tate problem and Kondo-like problems in the context of relevant bounda ry perturbations of boundary conformal field theories. (C) 1997 Elsevi er Science B.V.