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String Creation and Heterotic-Type I' Duality

O. Bergman, M. R. Gaberdiel, G. Lifschytz

TL;DR

This work establishes a detailed heterotic–Type I' duality in nine dimensions with Wilson lines, deriving a BPS spectrum for Type I' that is naturally interpreted as D0-brane plus winding states. The authors derive a precise map between heterotic and Type I' quantum numbers, showing that heterotic KK momentum corresponds to Type I' winding while heterotic winding maps to the D0-brane number, and they demonstrate that Type I' winding is always physical and supersymmetric under this map. They provide independent evidence for string creation when D8-branes cross D0-branes by tracing how BPS states evolve with the Wilson line, and they illustrate non-perturbative gauge enhancements to exceptional groups (e.g., $E_8$, $E_7$) at specific radii, consistent with the heterotic picture. The results yield predictions for the quantum mechanics of D0-branes in Type I' backgrounds and offer a non-perturbative cross-check of duality, with broader implications for M-theory/Matrix theory viewpoints on brane dynamics.

Abstract

The BPS spectrum of type I' string theory in a generic background is derived using the duality with the nine-dimensional heterotic string theory with Wilson lines. It is shown that the corresponding mass formula has a natural interpretation in terms of type I', and it is demonstrated that the relevant states in type I' preserve supersymmetry. By considering certain BPS states for different Wilson lines an independent confirmation of the string creation phenomenon in the D0-D8 system is found. We also comment on the non-perturbative realization of gauge enhancement in type I', and on the predictions for the quantum mechanics of type I' D0-branes.

String Creation and Heterotic-Type I' Duality

TL;DR

This work establishes a detailed heterotic–Type I' duality in nine dimensions with Wilson lines, deriving a BPS spectrum for Type I' that is naturally interpreted as D0-brane plus winding states. The authors derive a precise map between heterotic and Type I' quantum numbers, showing that heterotic KK momentum corresponds to Type I' winding while heterotic winding maps to the D0-brane number, and they demonstrate that Type I' winding is always physical and supersymmetric under this map. They provide independent evidence for string creation when D8-branes cross D0-branes by tracing how BPS states evolve with the Wilson line, and they illustrate non-perturbative gauge enhancements to exceptional groups (e.g., , ) at specific radii, consistent with the heterotic picture. The results yield predictions for the quantum mechanics of D0-branes in Type I' backgrounds and offer a non-perturbative cross-check of duality, with broader implications for M-theory/Matrix theory viewpoints on brane dynamics.

Abstract

The BPS spectrum of type I' string theory in a generic background is derived using the duality with the nine-dimensional heterotic string theory with Wilson lines. It is shown that the corresponding mass formula has a natural interpretation in terms of type I', and it is demonstrated that the relevant states in type I' preserve supersymmetry. By considering certain BPS states for different Wilson lines an independent confirmation of the string creation phenomenon in the D0-D8 system is found. We also comment on the non-perturbative realization of gauge enhancement in type I', and on the predictions for the quantum mechanics of type I' D0-branes.

Paper Structure

This paper contains 11 sections, 48 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Review of $D=9$ heterotic string theory
  3. Duality map and type I' BPS states
  4. Type I' BPS spectrum
  5. A condition on the winding number
  6. String creation and gauge enhancement
  7. D0-D8 strings
  8. Gauge enhancement
  9. Conclusions
  10. Lightest BPS states
  11. D8-branes in the bulk

Figures (3)

  • Figure 1: States corresponding to the weights (a) $\pm(1,-1)$, and (b) $\pm(1,1)$. The dashed vertical line represents an orientifold 8-plane and the solid vertical lines represent D8-branes.
  • Figure 5: $SO(14)\times U(1)\rightarrow E_8$. (a) spinor ${\bf 64}_+$ (b) and (c) give rise to the vector representation ${\bf 14}_+$.
  • Figure 6: $SO(12)\times U(1)\rightarrow E_7$ (a) spinor ${\bf 32}_+$. (b) is massive, and (c) is a singlet ${\bf 1}_+$.