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Global Type IIA Vacuum: A Unified Model for the Standard Model and Cosmology

Yang Liu

TL;DR

The paper builds a globally consistent Type IIA string framework on $T^6/\left(\mathbb{Z}_2 \times \mathbb{Z}_2\right)$ with intersecting D6-branes to realize an MSSM-like spectrum and to unify explanations for CP violation, baryogenesis, the electroweak hierarchy, and de Sitter uplifting via fluxes, Euclidean D2-instantons, and moduli stabilization. CP violation arises from both geometric Yukawa phases and instanton-induced phases $\phi_{RR}$, while baryon/lepton number violation stems from E2-instanton operators that also feed leptogenesis through a moduli-driven scenario. A three-step STU moduli stabilization with a controlled Minkowski-to-AdS shift and a dS uplift via anti-D6-branes yields a viable, metastable vacuum with a TeV-scale gravitino mass, enabling a consistent link between collider-scale flavor physics and cosmology. An explicit illustrative Model A demonstrates Yukawa textures, CKM mixing, CP violation, leptogenesis parameters, and proton stability within this unified setup, highlighting both the promise and the current simplifications (notably the need for a fully realistic Calabi–Yau compactification).

Abstract

We propose a unified framework within Type IIA string theory, based on a globally consistent intersecting D6-brane model compactified on a $T^6/(\mathbb{Z}_2 \times \mathbb{Z}_2)$ orientifold. The model realizes the MSSM-like spectrum providing a framework for addressing four fundamental problems: CP violation originates from both geometric phases in Yukawa couplings and non-perturbative phases induced by E2-instantons; the observed baryon asymmetry arises via instanton-mediated operators combined with moduli-driven leptogenesis; the electroweak hierarchy is stabilized through controlled SUSY breaking with a TeV-scale gravitino mass near a metastable vacuum; and a de Sitter uplift is achieved via anti-D6-branes in an STU moduli stabilization scheme. Crucially, the interplay of intersecting brane geometry, Euclidean D2-instantons, and flux-induced moduli potentials provides a coherent mechanism linking collider, flavor, and cosmological phenomena.

Global Type IIA Vacuum: A Unified Model for the Standard Model and Cosmology

TL;DR

The paper builds a globally consistent Type IIA string framework on with intersecting D6-branes to realize an MSSM-like spectrum and to unify explanations for CP violation, baryogenesis, the electroweak hierarchy, and de Sitter uplifting via fluxes, Euclidean D2-instantons, and moduli stabilization. CP violation arises from both geometric Yukawa phases and instanton-induced phases , while baryon/lepton number violation stems from E2-instanton operators that also feed leptogenesis through a moduli-driven scenario. A three-step STU moduli stabilization with a controlled Minkowski-to-AdS shift and a dS uplift via anti-D6-branes yields a viable, metastable vacuum with a TeV-scale gravitino mass, enabling a consistent link between collider-scale flavor physics and cosmology. An explicit illustrative Model A demonstrates Yukawa textures, CKM mixing, CP violation, leptogenesis parameters, and proton stability within this unified setup, highlighting both the promise and the current simplifications (notably the need for a fully realistic Calabi–Yau compactification).

Abstract

We propose a unified framework within Type IIA string theory, based on a globally consistent intersecting D6-brane model compactified on a orientifold. The model realizes the MSSM-like spectrum providing a framework for addressing four fundamental problems: CP violation originates from both geometric phases in Yukawa couplings and non-perturbative phases induced by E2-instantons; the observed baryon asymmetry arises via instanton-mediated operators combined with moduli-driven leptogenesis; the electroweak hierarchy is stabilized through controlled SUSY breaking with a TeV-scale gravitino mass near a metastable vacuum; and a de Sitter uplift is achieved via anti-D6-branes in an STU moduli stabilization scheme. Crucially, the interplay of intersecting brane geometry, Euclidean D2-instantons, and flux-induced moduli potentials provides a coherent mechanism linking collider, flavor, and cosmological phenomena.

Paper Structure

This paper contains 37 sections, 80 equations, 4 tables.

Table of Contents

  1. Introduction
  2. Four-forms in Type IIA orientifolds, model setup and consistency conditions
  3. Review of 4-forms in Type IIA orientifolds
  4. Setup and consistency conditions of Model A
  5. The role of a small flux parameter: $m \neq 0$
  6. CP violation from Yukawa and instanton phases
  7. Geometric Yukawa phases from brane path areas
  8. CKM matrix and Jarlskog invariant
  9. E2-instanton and the non-perturbative CP phase $\phi_{RR}$
  10. $\Delta B$, $\Delta L$ from $E2$-instanton operators
  11. Instanton wrapping cycles and charged zero-mode analysis
  12. Majorana mass terms and the effective lagrangian
  13. $QQQL$ operators and proton decay
  14. Simultaneous CP violation and baryon/lepton number violation
  15. Lagrangian structures and zero-modes
  16. ...and 22 more sections