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Orientifolds, hypercharge embeddings and the Standard Model

P. Anastasopoulos, T. P. T. Dijkstra, E. Kiritsis, A. N. Schellekens

TL;DR

<3-5 sentence high-level summary>This paper classifies how the Standard Model hypercharge can be embedded in orientifold gauge groups and systematically explores SM-like vacua in Gepner orientifolds using a combined bottom-up/top-down approach. It introduces a key parameter x that encodes hypercharge embeddings, and conducts a large-scale RCFT orientifold scan revealing 19345 chiral top-down SM spectra and about 1900 tadpole-satisfying solutions, with the x=1/2 (Madrid-type) embedding dominating. The work finds genuine supersymmetric SU(5) and flipped SU(5) examples and minimal Pati-Salam and trinification vacua, while showing strong suppression of configurations with chiral antisymmetric tensors and highlighting persistent mass-generation challenges in several promising embeddings. It also analyzes how CY topology influences SM realizations and discusses potential phenomenological implications, including family symmetries and neutrino masses.</3-5 sentence high-level summary>

Abstract

The embedding of the SM hypercharge into an orientifold gauge group is studied. Possible embeddings are classified, and a systematic construction of bottom-up configurations and top-down orientifold vacua is achieved, solving the tadpole conditions in the context of Gepner orientifolds. Some hypercharge embeddings are strongly preferred compared to others. Configurations with chiral antisymmetric tensors are suppressed. We find among others, genuine examples of supersymmetric SU(5), flipped SU(5), Pati-Salam and trinification vacua with no chiral exotics.

Orientifolds, hypercharge embeddings and the Standard Model

TL;DR

<3-5 sentence high-level summary>This paper classifies how the Standard Model hypercharge can be embedded in orientifold gauge groups and systematically explores SM-like vacua in Gepner orientifolds using a combined bottom-up/top-down approach. It introduces a key parameter x that encodes hypercharge embeddings, and conducts a large-scale RCFT orientifold scan revealing 19345 chiral top-down SM spectra and about 1900 tadpole-satisfying solutions, with the x=1/2 (Madrid-type) embedding dominating. The work finds genuine supersymmetric SU(5) and flipped SU(5) examples and minimal Pati-Salam and trinification vacua, while showing strong suppression of configurations with chiral antisymmetric tensors and highlighting persistent mass-generation challenges in several promising embeddings. It also analyzes how CY topology influences SM realizations and discusses potential phenomenological implications, including family symmetries and neutrino masses.</3-5 sentence high-level summary>

Abstract

The embedding of the SM hypercharge into an orientifold gauge group is studied. Possible embeddings are classified, and a systematic construction of bottom-up configurations and top-down orientifold vacua is achieved, solving the tadpole conditions in the context of Gepner orientifolds. Some hypercharge embeddings are strongly preferred compared to others. Configurations with chiral antisymmetric tensors are suppressed. We find among others, genuine examples of supersymmetric SU(5), flipped SU(5), Pati-Salam and trinification vacua with no chiral exotics.

Paper Structure

This paper contains 49 sections, 69 equations, 6 figures, 2 tables.

Table of Contents

  1. Introduction
  2. What we are looking for
  3. Classification of bottom-up embeddings
  4. Orientable configurations
  5. Charge Quantization
  6. Non-orientable configurations
  7. The cases $x=-\frac{1}{2}$ or $x=\frac{3}{2}$
  8. The case $x=1$
  9. Realizations with three brane stacks for $x=0$
  10. Realizations with three brane stacks for $x=\frac{1}{2}$
  11. Solutions with type E and F branes
  12. Solutions with type G branes
  13. Statistics of bottom-up configurations
  14. Three stacks: the $U(3)\times U(2)\times U(1)$ models
  15. Four stacks: $U(3)\times U(2)\times U(1)\times U(1)'$ Models
  16. ...and 34 more sections

Figures (6)

  • Figure 1: Chiral tensor distribution for all standard model configurations.
  • Figure 2: Number of chiral tensors and bi-fundamentals for a selection of branes.
  • Figure 3: Number of chiral and non-chiral tensors for all single branes.
  • Figure 4: Higgs pair distribution for all standard model configurations.
  • Figure 5: Right-handed neutrino distribution for all standard model configurations.
  • ...and 1 more figures