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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 (16 sections, 61 equations, 4 figures)

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.