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Getting just the Supersymmetric Standard Model at Intersecting Branes on the Z6-orientifold

Gabriele Honecker, Tassilo Ott

TL;DR

The paper demonstrates that globally N=1 supersymmetric configurations of intersecting D6-branes on the Z6 orientifold with fractional branes naturally funnel to a unique five-stack class that reproduces the MSSM-like chiral content with a massless hypercharge. By a detailed analysis of bulk and exceptional cycles, RR tadpoles, and Green-Schwarz couplings, it maps the open-string spectrum to explicit brane configurations, presenting two concrete realizations on the AAB and ABA lattices. It further shows that left-right symmetric variants arise in a separate class and discusses how brane recombination can realize the Higgs sector in some cases, while in others it is obstructed. The work provides a thorough geometric-engineering route to MSSM-like physics within type II string theory and outlines future directions for Yukawa structure, coupling unification, and SUSY breaking within these models.

Abstract

In this paper, globally N=1 supersymmetric configurations of intersecting D6-branes on the Z6-orientifold are discussed, involving also fractional branes. It turns out rather miraculously that one is led almost automatically to just ONE particular class of 5 stack models containing the SM gauge group, which all have the same chiral spectrum. The further discussion shows that these models can be understood as exactly the supersymmetric standard model without any exotic chiral symmetric/antisymmetric matter. The superpartner of the Higgs finds a natural explanation and the hypercharge remains massless. However, the non-chiral spectrum within the model class is very different and does not in all cases allow for a N=2 low energy field theoretical understanding of the necessary breaking U(1)xU(1)->U(1) along the Higgs branch, which is needed in order to get the standard Yukawa couplings. Also the left-right symmetric models belong to exactly one class of chiral spectra, where the two kinds of exotic chiral fields can have the interpretation of forming a composite Higgs. The aesthetical beauty of these models, involving only non-vanishing intersection numbers of an absolute value three, seems to be unescapable.

Getting just the Supersymmetric Standard Model at Intersecting Branes on the Z6-orientifold

TL;DR

The paper demonstrates that globally N=1 supersymmetric configurations of intersecting D6-branes on the Z6 orientifold with fractional branes naturally funnel to a unique five-stack class that reproduces the MSSM-like chiral content with a massless hypercharge. By a detailed analysis of bulk and exceptional cycles, RR tadpoles, and Green-Schwarz couplings, it maps the open-string spectrum to explicit brane configurations, presenting two concrete realizations on the AAB and ABA lattices. It further shows that left-right symmetric variants arise in a separate class and discusses how brane recombination can realize the Higgs sector in some cases, while in others it is obstructed. The work provides a thorough geometric-engineering route to MSSM-like physics within type II string theory and outlines future directions for Yukawa structure, coupling unification, and SUSY breaking within these models.

Abstract

In this paper, globally N=1 supersymmetric configurations of intersecting D6-branes on the Z6-orientifold are discussed, involving also fractional branes. It turns out rather miraculously that one is led almost automatically to just ONE particular class of 5 stack models containing the SM gauge group, which all have the same chiral spectrum. The further discussion shows that these models can be understood as exactly the supersymmetric standard model without any exotic chiral symmetric/antisymmetric matter. The superpartner of the Higgs finds a natural explanation and the hypercharge remains massless. However, the non-chiral spectrum within the model class is very different and does not in all cases allow for a N=2 low energy field theoretical understanding of the necessary breaking U(1)xU(1)->U(1) along the Higgs branch, which is needed in order to get the standard Yukawa couplings. Also the left-right symmetric models belong to exactly one class of chiral spectra, where the two kinds of exotic chiral fields can have the interpretation of forming a composite Higgs. The aesthetical beauty of these models, involving only non-vanishing intersection numbers of an absolute value three, seems to be unescapable.

Paper Structure

This paper contains 35 sections, 87 equations, 2 figures, 24 tables.

Table of Contents

  1. Introduction
  2. Geometry of the $T^6/{\mathbb Z}_6$ orbifold
  3. Bulk 3-cycles
  4. Exceptional 3-cycles
  5. An integral basis
  6. Orientifold projection
  7. Orientifold images of bulk cycles
  8. Orientifold images of exceptional cycles
  9. RR tadpole cancellation
  10. Supersymmetry conditions
  11. Supersymmetric bulk cycles
  12. Supersymmetry condition on exceptional cycles
  13. Massless open string spectrum: tree and loop amplitudes
  14. Boundary states for fractional intersecting branes
  15. Loop channel amplitudes
  16. ...and 20 more sections

Figures (2)

  • Figure 1: Fixed points of the $T^6/{\mathbb Z}_6$ orbifold. Full circles denote $\theta^2$ fixed points on $T^2_1 \times T^2_2$, empty circles additional $\theta^3$ fixed points. On $T^2_3$, the points 1,2,3 are fixed under $\theta$, the whole $T^2_3$ is fixed under $\theta^3$. The coordinates are depicted for the AAA torus. The details of the choices of complex structures are given in section \ref{['Subsec:OProjections']} and appendix \ref{['AppSec:BasisTori']}.
  • Figure 2: Geometrical intersections of branes $c$ and $(\theta^2 e)$ on the AAB torus. The gauge group is $U(1)_c \times U(1)_e$ if the branes are displaced from the origin on $T^2_3$. Remember that the $\mathcal{R}$ invariant plane lies along $\pi_1 \otimes \pi_3 \otimes (\pi_5+\pi_6)$ with the notation as in figure \ref{['Fig:Z6torifixedpoints']}.