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Exact Standard Model Compactifications from Intersecting Branes

Christos Kokorelis

TL;DR

The paper addresses constructing exact Standard Model-like vacua from intersecting D6-branes on orientifolded T^6 in Type I string theory. Hypercharge is realized as a massless linear combination of U(1)s, while a generalized Green-Schwarz mechanism cancels U(1) anomalies and gives masses to unwanted U(1)s; certain intersections preserve N=1 SUSY to generate singlets that break the remaining extra U(1)s, yielding the SM at low energy. Neutrinos are Dirac due to gauged lepton number, and proton stability follows from gauged baryon number; small neutrino masses arise via a PQ-like symmetry and higher-dimension operators, with the string scale potentially accessible. The work provides explicit tadpole-consistent six-stack constructions, analyzes anomaly cancellation and the Higgs sector from open strings, and predicts exactly two supersymmetric particles (the superpartners of the right-handed neutrinos), while discussing stability issues and future Calabi-Yau embeddings.

Abstract

We construct six stack D6-brane vacua (non-supersymmetric) that have at low energy exactly the standard model (with right handed neutrinos). The construction is based on D6-branes intersecting at angles in $D = 4$ type toroidal orientifolds of type I strings. Three U(1)'s become massive through their couplings to RR fields and from the three surviving massless U(1)'s at low energies, one is the standard model hypercharge generator. The two extra massless U(1)'s get broken, as suggested recently (hep-th/0205147), by requiring some intersections to respect N=1 supersymmetry thus supporting the appearance of massless charged singlets. Proton and lepton number are gauged symmetries and their anomalies are cancelled through a generalized Green-Schwarz mechanism that gives masses to the corresponding gauge bosons through couplings to RR fields. Thus proton is stable and neutrinos are of Dirac type with small masses as a result of a PQ like-symmetry. The models predict the existence of only two supersymmetric particles, superpartners of $ν_R$'s.

Exact Standard Model Compactifications from Intersecting Branes

TL;DR

The paper addresses constructing exact Standard Model-like vacua from intersecting D6-branes on orientifolded T^6 in Type I string theory. Hypercharge is realized as a massless linear combination of U(1)s, while a generalized Green-Schwarz mechanism cancels U(1) anomalies and gives masses to unwanted U(1)s; certain intersections preserve N=1 SUSY to generate singlets that break the remaining extra U(1)s, yielding the SM at low energy. Neutrinos are Dirac due to gauged lepton number, and proton stability follows from gauged baryon number; small neutrino masses arise via a PQ-like symmetry and higher-dimension operators, with the string scale potentially accessible. The work provides explicit tadpole-consistent six-stack constructions, analyzes anomaly cancellation and the Higgs sector from open strings, and predicts exactly two supersymmetric particles (the superpartners of the right-handed neutrinos), while discussing stability issues and future Calabi-Yau embeddings.

Abstract

We construct six stack D6-brane vacua (non-supersymmetric) that have at low energy exactly the standard model (with right handed neutrinos). The construction is based on D6-branes intersecting at angles in type toroidal orientifolds of type I strings. Three U(1)'s become massive through their couplings to RR fields and from the three surviving massless U(1)'s at low energies, one is the standard model hypercharge generator. The two extra massless U(1)'s get broken, as suggested recently (hep-th/0205147), by requiring some intersections to respect N=1 supersymmetry thus supporting the appearance of massless charged singlets. Proton and lepton number are gauged symmetries and their anomalies are cancelled through a generalized Green-Schwarz mechanism that gives masses to the corresponding gauge bosons through couplings to RR fields. Thus proton is stable and neutrinos are of Dirac type with small masses as a result of a PQ like-symmetry. The models predict the existence of only two supersymmetric particles, superpartners of 's.

Paper Structure

This paper contains 11 sections, 54 equations, 1 figure, 4 tables.

Table of Contents

  1. Introduction
  2. Exact Standard model compactifications from Intersecting branes
  3. U(1) anomaly cancelation
  4. Higgs mechanism on open string sectors
  5. The angle structure
  6. Tachyon Higgs mechanism
  7. Preserving $N=1$ SUSY at intersections
  8. Neutrino couplings and masses
  9. Conclusions and future directions
  10. Acknowledgements
  11. Appendix A

Figures (1)

  • Figure 1: Assignment of angles between D6-branes on the six stack type I model giving rise to the standard model at low energies. The angles between branes are shown on a product of $T^2 \times T^2 \times T^2$. We have chosen $\beta^1 =\beta^2 =1$, $n_b^1, n_c^1, n_a^2, n_d^2 >0$, $\epsilon = {\tilde{\epsilon}} = 1$.