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Aspects of Type I String Phenomenology

L. E. Ibáñez, C. Muñoz, S. Rigolin

TL;DR

This paper analyzes four-dimensional $N=1$ Type IIB orientifolds with Dp-branes as a framework for unifying the Standard Model with gravity. It elucidates how brane configurations and compactification scales set the string scale $M_I$, the Planck scale $M_{ m Pl}$, and unification scales $M_X$, proposing that the $M_W/M_{ m Pl}$ hierarchy can arise geometrically and that dilaton/moduli fields can mediate SUSY breaking. The authors derive the low-energy supergravity Lagrangian, map out soft SUSY-breaking terms, and examine the roles of anomalous $U(1)$s and twisted moduli, including a mechanism by which singularities enable precocious gauge coupling unification at a low string scale. They also explore non-universality of soft terms across brane sectors and discuss how twisted moduli can influence gauge coupling running, offering potential routes to unification without high-scale GUTs while noting phenomenological challenges such as proton stability and precision unification.

Abstract

We study different phenomenological aspects of compact, D=4, N=1 Type IIB orientifolds considered as models for unification of the standard model and gravity. We discuss the structure of the compactification, string and unification scales depending on the different possible D-brane configurations. It is emphasized that in the context of Type I models the $M_W/M_{Planck}$ hierarchy problem is substantially alleviated and may be generated by geometrical factors. We obtain the effective low-energy supergravity Lagrangian and derive the form of soft SUSY-breaking terms under the assumption of dilaton/moduli dominance. We also discuss the role of anomalous U(1)'s and of twisted moduli in this class of theories. A novel mechanism based on the role of singularities is suggested to achieve consistency with gauge coupling unification in low string scale models.

Aspects of Type I String Phenomenology

TL;DR

This paper analyzes four-dimensional Type IIB orientifolds with Dp-branes as a framework for unifying the Standard Model with gravity. It elucidates how brane configurations and compactification scales set the string scale , the Planck scale , and unification scales , proposing that the hierarchy can arise geometrically and that dilaton/moduli fields can mediate SUSY breaking. The authors derive the low-energy supergravity Lagrangian, map out soft SUSY-breaking terms, and examine the roles of anomalous s and twisted moduli, including a mechanism by which singularities enable precocious gauge coupling unification at a low string scale. They also explore non-universality of soft terms across brane sectors and discuss how twisted moduli can influence gauge coupling running, offering potential routes to unification without high-scale GUTs while noting phenomenological challenges such as proton stability and precision unification.

Abstract

We study different phenomenological aspects of compact, D=4, N=1 Type IIB orientifolds considered as models for unification of the standard model and gravity. We discuss the structure of the compactification, string and unification scales depending on the different possible D-brane configurations. It is emphasized that in the context of Type I models the hierarchy problem is substantially alleviated and may be generated by geometrical factors. We obtain the effective low-energy supergravity Lagrangian and derive the form of soft SUSY-breaking terms under the assumption of dilaton/moduli dominance. We also discuss the role of anomalous U(1)'s and of twisted moduli in this class of theories. A novel mechanism based on the role of singularities is suggested to achieve consistency with gauge coupling unification in low string scale models.

Paper Structure

This paper contains 16 sections, 61 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Type IIB orientifolds, Dp-branes and T-duality
  3. D-branes, string scale and gauge coupling unification in Type I $D=4$ string vacua
  4. D-branes, string scale and Planck mass
  5. Gauge coupling unification with an isotropic compact space
  6. Non-isotropic compactifications
  7. Embedding $SU(3)$ and $SU(2)$ within different sets of p-branes
  8. Micro gauge/Yukawa interactions
  9. The generation of the $M_W/M_{Planck}$ hierarchy
  10. Gaugino condensation
  11. Effective low-energy Lagrangian in $D=4$ $N=1$ compact orientifold models
  12. Soft SUSY-breaking terms from dilaton/moduli spurions
  13. General p-brane configurations
  14. Configurations with 9-branes and one set of 5-branes
  15. Anomalous $U(1)$'s, twisted moduli and precocious gauge coupling unification
  16. ...and 1 more sections

Figures (4)

  • Figure 1: Running of the dimensionless gravitational coupling and gauge couplings with energy. The SM is embedded in a $9$($3$)-brane sector.
  • Figure 2: Running of the dimensionless gravitational coupling and gauge couplings with energy. The SM is embedded in a $7$($5$)-brane sector.
  • Figure 3: Scalar (C) and gaugino ($\tilde{g}$) squared masses in unit of $m^2_{3/2}$ versus $\sin^2 \theta$ for S/overall modulus ($\Theta_i = 1/\sqrt{3}$) SUSY breaking when $9$-branes and one set of $5_1$-branes are present. The solid lines (with only the scalar fields $C_i^9$) correspond to the situation where only $9$-brane sectors are present.
  • Figure 4: Scalar (C) and gaugino ($\tilde{g}$) squared masses in unit of $m^2_{3/2}$ versus $\sin^2 \theta$ for S/$T_1$ ($\Theta_1 =1$) SUSY breaking when $9$-branes and one set of $5_1$-branes are present. The solid lines (with only the scalar fields $C_i^9$) correspond to the situation where only $9$-brane sectors are present.