Confinement on the Brane

TL;DR

The paper addresses how open-string degrees of freedom are eliminated during brane-anti-brane annihilation by proposing a non-perturbative confinement mechanism that removes the unbroken world-volume $U(1)$. It combines perturbative insights (Sen's tachyon-based action) with a dual Higgs/confinement framework, showing through the D2-anti-D2 system in M-theory that the confined electric flux forms a string identified with the fundamental string. It extends the analysis to multiple branes and unstable branes, develops a geometric confinement picture (via winding on compact circles), and investigates confinement at weak string coupling, including explicit treatment of the $p=1$ case and the role of instanton effects for $p=2$. The work connects open-string tachyon condensation to non-perturbative world-volume dynamics, aiming to explain how annihilation converts open-string degrees of freedom into the closed-string spectrum and highlighting the emergence of fundamental strings as confining flux tubes. The results provide a cohesive scenario where both perturbative and non-perturbative mechanisms cooperate to resolve the unbroken $U(1)$ puzzle and open pathways for further study of confinement in string theory.

Abstract

A non-perturbative confinement mechanism has been proposed to explain the fate of the unbroken gauge group on the world-volume of annihilating D-brane-anti-D-brane pairs. In this paper, we examine this phenomenon closely from several different perspectives. Existence of the confinement mechanism is most easily seen by noticing that the fundamental string emerges as the confined electric flux string at the end of the annihilation process. After reviewing the confinement proposal in general, this is shown explicitly in the D2-anti-D2 case in the M-theory limit. Finally, we address the crucial issue of whether and how confinement occurs in the weakly coupled limit of string theory.

Figures (5)

• Figure 1: An M2-brane winding around $X^{11}$ once and an anti-M2-brane with no winding (left). On the D2-brane, the winding translates into a unit of electric flux (right).
• Figure 2: Most of the M2-brane annihilates with the anti-M2-brane, but part of it remains and winds around $X^{11}$. The result is a single longitudinal M2-brane along $X^{11}$ (left). Seen from the original transverse world-volume of the M2-brane (right), this translates into a tightly confined flux string.
• Figure 3: Any configuration attains minimum energy density (\ref{['tension1']}) as long as $\sigma(x^2)$ is a monotonic function. Furthermore, the charge $\Delta\sigma$ is not quantized.
• Figure 4: By the instanton effect, the charge $|\Delta\sigma|$ is quantized and the energy density (\ref{['tension2']}) is minimized for the completely squeezed configuration. This density, or the tension of the resulting string, is proportional to the charge.
• Figure 5: The tachyon potential (a), and the tachyon-magnetic-tachyon potential at the vacuum value of $T=T_0$ (b).