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Stable Non-BPS States in String Theory

Ashoke Sen

TL;DR

The paper investigates stable non-BPS states in string theory and uses duality symmetries to determine their strong-coupling masses in select D$p$-brane–$O$p$-plane configurations. By mapping to M-theory and Seiberg-Witten frameworks, it derives explicit strong-coupling mass scalings for $p=6$ and $p=7$ (and a weaker, but controlled, result for $p=4$), revealing distinct growth/decay behaviors such as $m \sim ({\\pi}/4)(\\alpha')^{-1/2} g_S$ for $p=6$ and an exponentially suppressed form $m \sim g_S^{-1/4} \exp(-\\pi/(3 g_S))$ for $p=7$. The work also discusses unresolved cases (e.g., $p=3$, $p=5$, and higher) and presents speculations that missing states may originate from non-supersymmetric D0-brane–like objects in orientifold/orbifold setups, highlighting the potential for dualities to reveal non-BPS spectra and the need for further non-perturbative techniques. Overall, the paper advances understanding of non-BPS spectra in strong coupling regimes and sketches concrete mass formulas and geometric pictures for several D$p$-brane–$O$p$-plane systems.

Abstract

Many string theories contain states which are not BPS, but are stable due to charge conservation. In many cases the description of these states in the strong coupling limit remains unknown despite the existence of a weakly coupled dual theory. However, we show that in some cases duality symmetries in string theory do enable us to identify these states in the strong coupling limit and calculate their masses. We also speculate that in some of the other cases the missing states might arise from non-supersymmetric analog of D0-branes.

Stable Non-BPS States in String Theory

TL;DR

The paper investigates stable non-BPS states in string theory and uses duality symmetries to determine their strong-coupling masses in select D-brane–pp=6p=7p=4m \sim ({\\pi}/4)(\\alpha')^{-1/2} g_Sp=6m \sim g_S^{-1/4} \exp(-\\pi/(3 g_S))p=7p=3p=5pO-plane systems.

Abstract

Many string theories contain states which are not BPS, but are stable due to charge conservation. In many cases the description of these states in the strong coupling limit remains unknown despite the existence of a weakly coupled dual theory. However, we show that in some cases duality symmetries in string theory do enable us to identify these states in the strong coupling limit and calculate their masses. We also speculate that in some of the other cases the missing states might arise from non-supersymmetric analog of D0-branes.

Paper Structure

This paper contains 7 sections, 55 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Dirichlet 6-brane on Top of an Orientifold 6-plane
  3. Dirichlet 7-brane on Top of an Orientifold 7-plane
  4. Dirichlet 4-brane on Top of an Orientifold 4-plane
  5. Other D$p$-brane $-$ O$p$-plane Systems
  6. Some Speculations about the Missing States
  7. Computation of the Coefficient $C$

Figures (10)

  • Figure 1: D7-O7 system with D7-brane far away from the O7-plane. The dashed lines indicate the path along which the seven branes are viewed.
  • Figure 2: A different view of the configuration shown in Fig.\ref{['f1']}.
  • Figure 3: An open string configuration representing a state carrying SO(2) charge.
  • Figure 4: The minimal energy configuration of open string network representing a state carrying SO(2) charge. Although in this figure we have displayed the open strings to be lying along straight lines, they actually lie along geodesics described in eq.(\ref{['ea9']}).
  • Figure 5: The 7-brane configuration for coincident D7-O7 system.
  • ...and 5 more figures