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Hořava-Witten theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ as type 0 orientifold

Chiara Altavista, Edoardo Anastasi, Salvatore Raucci, Angel M. Uranga, Chuying Wang

Abstract

We investigate dualities between ${\mathbf{Z}}_2$ quotients of recently proposed compactifications of M-theory on `quantum geometries' of the form ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ and 10d orientifolds of type 0A and 0B string theories. In particular, we relate the Hořava-Witten theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ to a 0B orientifold with gauge group $SO(16)^4$. The resulting dictionary provides a geometric explanation for characteristic features of the 0B orientifold, such as the doubling of the gauge group, while the perturbative spectrum of the 0B orientifold indicates the emergence of novel M-theoretic degrees of freedom associated with the junction point. The 0B orientifold further reveals the existence of two variants of the theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$, corresponding to equal vs opposite (i.e., standard vs Fabinger-Hořava) orientations of the $E_8$ walls. We also analyze additional 0A and 0B orientifolds whose open string sectors do not arise from higher-dimensional gauge fields in M-theory and whose microscopic interpretation remains an open problem.

Hořava-Witten theory on ${\mathbf{S}}^1\vee{\mathbf{S}}^1$ as type 0 orientifold

Abstract

We investigate dualities between quotients of recently proposed compactifications of M-theory on `quantum geometries' of the form and 10d orientifolds of type 0A and 0B string theories. In particular, we relate the Hořava-Witten theory on to a 0B orientifold with gauge group . The resulting dictionary provides a geometric explanation for characteristic features of the 0B orientifold, such as the doubling of the gauge group, while the perturbative spectrum of the 0B orientifold indicates the emergence of novel M-theoretic degrees of freedom associated with the junction point. The 0B orientifold further reveals the existence of two variants of the theory on , corresponding to equal vs opposite (i.e., standard vs Fabinger-Hořava) orientations of the walls. We also analyze additional 0A and 0B orientifolds whose open string sectors do not arise from higher-dimensional gauge fields in M-theory and whose microscopic interpretation remains an open problem.

Paper Structure

This paper contains 28 sections, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Overview of the ingredients
  3. M-theory on S1 V S1 in a nutshell
  4. From M-theory to 10d type 0A
  5. From M-theory to 10d type 0B
  6. Type 0 orientifolds
  7. Orientifolds of type 0A
  8. Orientifolds of type 0B
  9. The $\Omega$ orientifold:
  10. The $\Omega(-1)^{F^s_L}$ orientifold:
  11. The $\Omega(-1)^{F^w_L}$ orientifold:
  12. The orientifold of type 0A from M-theory on S1 V S1
  13. Type 0A orientifold by Omega and its M-theory description
  14. Other Z2 symmetries
  15. The action (-1)FwL as exchange of M-theory circles in S1 V S1
  16. ...and 13 more sections

Figures (3)

  • Figure 1: Resolutions of ${\bf {S}}^1\vee{\bf {S}}^1$ and the corresponding DRP (disconnected resolution property) and SSP (strong smoothness property), the latter being a combination of two CRPs (connected resolution properties).
  • Figure 2: Structure of the spectrum of the 10d 0B orientifold for the set of four kinds of D9-branes (labelled $o$, $v$, $c$, $s$, as in Angelantonj:2002ct, or $1,2,3,4$, as in Dudas:2001wd. The dashed lines correspond to bifundamental tachyons, and the solid lines are bifundamental fermions (with chirality indicated by signs).
  • Figure 3: a) Two possible inequivalent ways to distribute the gauge branes among the two boundaries of the interval in the 0A orientifold with $SO(16)^2$ symmetry at each boundary. The HW distribution (separating as indicated by the light red line) corresponds to taking the branes $o$, $v$ (namely $1,2$) at one boundary and $c$, $s$ (namely $3,4$) at the other. The only surviving fields in each boundary are tachyons in the bifundamental of the $SO(16)^2$ at the corresponding boundary. On the other hand, the FH distribution (separating as indicated by the light blue line) corresponds to taking the branes $o$, $s$ (namely $1,4$) at one boundary and $v$, $c$ (namely $2,3$) at the other. The only surviving fields in each boundary are fermions in the bifundamental of the $SO(16)^2$ at the corresponding boundary. b) Inclusion of the two kinds of D0-branes (in violet and green) in the type 0A orientifold, with lines indicating their fermion zero modes.