Stable Non-BPS Bound States of BPS D-branes

TL;DR

S-duality in type IIB predicts a stable non-BPS bound state on a $Z_2$ orbifold five-plane; the paper derives its mass by analyzing a pair of D-strings carrying the same twisted-sector charge and identifying a tachyonic mode signaling bound-state formation. Using boundary-state techniques, Sen constructs D-string configurations ending on orbifold planes, including twisted-sector contributions, and computes open-closed string amplitudes to extract the mass relation $m_{++}= (\sqrt{2\alpha'}\,g)^{-1}$ in the string metric, with a dual expression $\tilde{m}_{++}= (\sqrt{2\alpha'})^{-1}\tilde{g}^{1/2}$ in the dual theory. The work then extends to type IIB on $(\mathbb{R}^{8,1}\times S^1)/Z_2$ with two fixed planes, showing eight D-strings between planes and identifying critical radii $R_c$ and $R_c'$ where tachyon condensation occurs, yielding the same bound-state mass and illustrating R-independence in certain limits. Overall, the results realize a concrete, boundary-state-based mechanism for non-BPS bound states protected by twisted-sector charges and S-duality, highlighting tachyon condensation as the binding mechanism and linking IIB and dual descriptions.

Abstract

S-duality symmetry of type IIB string theory predicts the existence of a stable non-BPS state on an orbifold five plane of the type IIB theory if the orbifold group is generated by the simultaneous action of (-1)^{F_L} and the reversal of sign of the four coordinates transverse to the orbifold plane. We calculate the mass of this state by starting from a pair of D-strings carrying the same charge as this state, and then identifying the point in the moduli space where this pair develops a tachyonic mode, signalling the appearance of a bound state of this configuration into the non-BPS state.

Figures (8)

• Figure 1: Open string configuration giving charged state on the world-volume of the D5-brane O5-plane system. The $\circ$ denotes the location of the O5-plane and the D denotes the location of the D5-brane.
• Figure 2: Four possible configurations of fundamental string ending on a D5-brane $-$ O5-plane system.
• Figure 3: S-dual of the configurations shown in Fig.\ref{['f2']}. Here the little square denotes the location of the orbifold plane.
• Figure 4: Superposition of the configurations shown in Fig.\ref{['f3']}(a) and (d).
• Figure 5: The tachyon field on the D-string - anti-D-string pair as a function of distance $x$ from the orbifold plane.