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

TL;DR

This paper analyzes bound states of p- and (p+2)-branes using magnetic flux and perturbative methods, confirming BPS mass predictions and exploring extensions to multiple branes and related gauge configurations.

Contribution

It introduces a perturbative approach to study brane bound states with magnetic flux, validating BPS mass formulas and discussing extensions beyond leading order.

Findings

Leading order vacuum energy matches BPS mass predictions.

Perturbative analysis is valid in large F limit for single and multiple branes.

Connections to boundary conformal field theory and gauge symmetry are discussed.

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.