On the Bound States of p- and (p+2)-Branes

TL;DR

The paper analyzes bound states between D-p-branes and D-(p+2)-branes by examining tachyonic open-string modes under a large magnetic flux, establishing a perturbative 1/$F$ expansion and showing that the leading quartic tachyon potential reproduces the BPS binding energies for various $(N,m)$ configurations. It uses both direct and T-dual pictures, including toron configurations and a Cartan-algebra approach, to derive ground states that saturate the BPS mass formula, and demonstrates that higher-order corrections do not alter the minimum energy while clarifying the surviving gauge symmetries. The results connect to boundary conformal field theory through nearly marginal boundary perturbations and hint at nontrivial fixed points predicted by string dualities, with broader implications for more complex brane systems and Kondo-like phenomena. Overall, the work provides a coherent,_dual-picture account of brane bound-state formation driven by tachyon condensation and its compatibility with BPS expectations and duality symmetries.

Abstract

We study bound states of D-p-branes and D-(p+2)-branes. By switching on 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 potential of the tachyonic state from the open string stretched between the p- and (p+2)-brane gives a vacuum energy which agrees with the prediction of the BPS mass formula for the bound state. We generalize the discussion to the case of m p-branes plus 1 (p+2)-brane with magnetic field. The T dual picture of this, namely several (p+2)-branes carrying some p-brane charges through magnetic flux is also discussed, where the perturbative treatment is available in the small F limit. We show that once again, in the same approximation, the tachyon condensates give rise to the correct BPS mass formula. The role of 't Hooft's toron configurations in the extension of the above results beyond the quartic approximation as well as the issue of the unbroken gauge symmetries are discussed. We comment on the connection between the present bound state problem and Kondo-like problems in the context of relevant boundary perturbations of boundary conformal field theories.