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Non-BPS States and Branes in String Theory

Ashoke Sen

TL;DR

This work surveys non-BPS states and branes in string theory, detailing unstable non-BPS D-branes in type II theories and their tachyonic instabilities, as well as stable non-BPS branes arising on orbifolds and orientifolds. It develops two complementary viewpoints: non-BPS branes as brane–antibrane tachyon condensates and BPS/non-BPS branes as tachyonic kink solitons, connecting these to K-theory classifications of D-brane charges. The paper also analyzes the spectrum of stable non-BPS states on D-brane–orientifold plane systems, providing strong-coupling descriptions via M-theory and dual string theories, and discusses related developments such as boundary-state formalisms and K-theory, while highlighting open questions and future directions. Overall, it lays a cohesive framework linking tachyon dynamics, brane descent relations, and nonperturbative dualities to understand non-BPS sectors in string theory and their mathematical structure.

Abstract

We review the recent developments in our understanding of non-BPS states and branes in string theory. The topics include 1) construction of unstable non-BPS D-branes in type IIA and type IIB string theories, 2) construction of stable non-BPS D-branes on various orbifolds and orientifolds of type II string theories, 3) description of BPS and non-BPS D-branes as tachyonic soliton solutions on brane-antibrane pair of higher dimension, and 4) study of the spectrum of non-BPS states and branes on a system of coincident D-brane - orientifold plane system. Some other related results are also discussed briefly.

Non-BPS States and Branes in String Theory

TL;DR

This work surveys non-BPS states and branes in string theory, detailing unstable non-BPS D-branes in type II theories and their tachyonic instabilities, as well as stable non-BPS branes arising on orbifolds and orientifolds. It develops two complementary viewpoints: non-BPS branes as brane–antibrane tachyon condensates and BPS/non-BPS branes as tachyonic kink solitons, connecting these to K-theory classifications of D-brane charges. The paper also analyzes the spectrum of stable non-BPS states on D-brane–orientifold plane systems, providing strong-coupling descriptions via M-theory and dual string theories, and discusses related developments such as boundary-state formalisms and K-theory, while highlighting open questions and future directions. Overall, it lays a cohesive framework linking tachyon dynamics, brane descent relations, and nonperturbative dualities to understand non-BPS sectors in string theory and their mathematical structure.

Abstract

We review the recent developments in our understanding of non-BPS states and branes in string theory. The topics include 1) construction of unstable non-BPS D-branes in type IIA and type IIB string theories, 2) construction of stable non-BPS D-branes on various orbifolds and orientifolds of type II string theories, 3) description of BPS and non-BPS D-branes as tachyonic soliton solutions on brane-antibrane pair of higher dimension, and 4) study of the spectrum of non-BPS states and branes on a system of coincident D-brane - orientifold plane system. Some other related results are also discussed briefly.

Paper Structure

This paper contains 21 sections, 52 equations, 14 figures.

Table of Contents

  1. Introduction
  2. Unstable Non-BPS D-branes in Type II String Theories
  3. BPS D-branes in type II string theories
  4. Non-BPS D-branes in type II string theories
  5. BPS D-branes from non-BPS D-branes
  6. Stable Non-BPS D-branes on Type II Orbifolds and Orientifolds
  7. Type I D-particle
  8. D-branes wrapped on non-supersymmetric cycles of K3 orbifold
  9. D-branes as Tachyonic Kink Solutions
  10. Non-BPS D-brane as tachyonic kink on the brane-antibrane pair
  11. The BPS D-brane as the tachyonic kink on the non-BPS D-brane
  12. Stable Non-BPS Branes on the D-brane $-$ Orientifold Plane System
  13. Summary of the results
  14. Strong coupling description of electrically charged states and magnetically charged branes
  15. Electrostatic self-energy of the electrically charged non-BPS particle on the D3-brane $-$ O3-plane system
  16. ...and 6 more sections

Figures (14)

  • Figure 1: Open strings ending on a BPS D-brane.
  • Figure 2: Open strings living on a coincident D-brane anti-D-brane pair. Although for clarity we have displayed the brane and the anti-brane to be spatially separated, we shall analyse the case where they coincide.
  • Figure 3: The disk amplitude for two point function of the graviton and translation mode of the D-brane.
  • Figure 5: Relationship between BPS and non-BPS D-branes in type II string theories. The horizontal arrow represents the effect of modding out the theory by $(-1)^{F_L}$.
  • Figure 6: The D0-${\bar{\rm D}}$0 brane configuration obtained by marginal deformation of the non-BPS D-string wrapped along $x^9$.
  • ...and 9 more figures