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Getting just the Standard Model at Intersecting Branes

L. E. Ibanez, F. Marchesano, R. Rabadan

TL;DR

Ibáñez, Marchesano, and Rabadán construct explicit intersecting D6-brane configurations on an orientifolded $T^6$ that yield the Standard Model spectrum with three generations and no extra massless exotics. Anomaly cancellation is achieved via a generalized Green-Schwarz mechanism, rendering three of the four initial $U(1)$ factors massive while leaving hypercharge massless, and B and L as (perturbative) global symmetries that protect proton stability and forbid Majorana neutrino masses. The models feature a MSSM-like Higgs sector with masses and couplings tied to geometric data, and Yukawa/gauge couplings that arise from worldsheet areas and brane lengths, enabling hierarchical fermion masses and non-unified couplings. The work also addresses stability (absence of tachyons over wide moduli ranges), predicts a spectrum of heavy states beyond the SM, and discusses implications for TeV-scale strings and future phenomenology.

Abstract

We present what we believe are the first specific string (D-brane) constructions whose low-energy limit yields just a three generation $SU(3)\times SU(2)\times U(1)$ standard model with no extra fermions nor U(1)'s (without any further effective field theory assumption). In these constructions the number of generations is given by the number of colours. The Baryon, Lepton and Peccei-Quinn symmetries are necessarily gauged and their anomalies cancelled by a generalized Green-Schwarz mechanism. The corresponding gauge bosons become massive but their presence guarantees automatically proton stability. There are necessarily three right-handed neutrinos and neutrino masses can only be of Dirac type. They are naturally small as a consequence of a PQ-like symmetry. There is a Higgs sector which is somewhat similar to that of the MSSM and the scalar potential parameters have a geometric interpretation in terms of brane distances and intersection angles. Some other physical implications of these constructions are discussed.

Getting just the Standard Model at Intersecting Branes

TL;DR

Ibáñez, Marchesano, and Rabadán construct explicit intersecting D6-brane configurations on an orientifolded that yield the Standard Model spectrum with three generations and no extra massless exotics. Anomaly cancellation is achieved via a generalized Green-Schwarz mechanism, rendering three of the four initial factors massive while leaving hypercharge massless, and B and L as (perturbative) global symmetries that protect proton stability and forbid Majorana neutrino masses. The models feature a MSSM-like Higgs sector with masses and couplings tied to geometric data, and Yukawa/gauge couplings that arise from worldsheet areas and brane lengths, enabling hierarchical fermion masses and non-unified couplings. The work also addresses stability (absence of tachyons over wide moduli ranges), predicts a spectrum of heavy states beyond the SM, and discusses implications for TeV-scale strings and future phenomenology.

Abstract

We present what we believe are the first specific string (D-brane) constructions whose low-energy limit yields just a three generation standard model with no extra fermions nor U(1)'s (without any further effective field theory assumption). In these constructions the number of generations is given by the number of colours. The Baryon, Lepton and Peccei-Quinn symmetries are necessarily gauged and their anomalies cancelled by a generalized Green-Schwarz mechanism. The corresponding gauge bosons become massive but their presence guarantees automatically proton stability. There are necessarily three right-handed neutrinos and neutrino masses can only be of Dirac type. They are naturally small as a consequence of a PQ-like symmetry. There is a Higgs sector which is somewhat similar to that of the MSSM and the scalar potential parameters have a geometric interpretation in terms of brane distances and intersection angles. Some other physical implications of these constructions are discussed.

Paper Structure

This paper contains 14 sections, 45 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. The standard model intersection numbers
  3. D6-branes intersecting at angles
  4. D6-branes on a torus
  5. Orientifolds
  6. $U(1)$ Anomaly cancellation
  7. Searching for the standard model
  8. Absence of tachyons and stability of the configurations
  9. Spectrum of massive particles beyond the SM
  10. The Higgs sector and electroweak symmetry breaking
  11. The Yukawa and gauge coupling constants
  12. Final comments and outlook
  13. Appendix I
  14. Appendix II

Figures (5)

  • Figure 1: The $\Omega{\cal R}$ world sheet parity takes one set of branes specified by $(n_i,m_i)$ to another set $(n_i,-m_i)$. The dashed line represent the direction where the O6-plane lives.
  • Figure 2: The region inside the tetrahedron has no tachyons. Faces, edges and vertices represent respectively, ${\cal N} = 1$, ${\cal N} = 2$ and ${\cal N} = 4$ systems at the given intersection.
  • Figure 3: Definition of the angles between the different branes on the three tori. We have selected a particular setting where $n_a^2,n_b^1,n_c^1,n_d^2 > 0$, $\epsilon = -1$ and $\beta^1 = 1/2$, $\beta^2= 1$.
  • Figure 4: Each rectangle represents a two torus. There are two branes: one is represented by a straight black line and the other by a dashed line. The curved lines represent strings ending on the D-branes.
  • Figure 6: One loop contribution to gaugino masses.