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U(1) Mediation of Flux Supersymmetry Breaking

Thomas W. Grimm, Albrecht Klemm

TL;DR

This work demonstrates how a light $U(1)$ vector multiplet, arising from RR sector modes in Type IIB string theory, can mediate SUSY breaking between a hidden flux sector and a visible D-brane sector in non-Kähler compactifications. The mediation mechanism relies on St"uckelberg couplings and a careful topological linking of hidden and visible cycles via non-Kähler resolutions, orientifolds, and geometric transitions. The authors develop a detailed four-dimensional ${\cal N}=1$ effective action, including complex-structure and non-K"ahler moduli, D-terms, and flux-induced superpotentials, and they construct explicit compact geometries (with del Pezzo surfaces and ADE singularities) that realize the desired mediation. They also show how toric techniques and Lie-algebraic data control the global connections between sectors, enabling concrete model-building prospects in string phenomenology and offering a framework to study scale and sequestering effects in SUSY-breaking scenarios.

Abstract

We study the mediation of supersymmetry breaking triggered by background fluxes in Type II string compactifications with N=1 supersymmetry. The mediation arises due to an U(1) vector multiplet coupling to both a hidden supersymmetry breaking flux sector and a visible D-brane sector. The required internal manifolds can be constructed by non-Kaehler resolutions of singular Calabi-Yau manifolds. The effective action encoding the U(1) coupling is then determined in terms of the global topological properties of the internal space. We investigate suitable local geometries for the hidden and visible sector in detail. This includes a systematic study of orientifold symmetries of del Pezzo surfaces realized in compact geometries after geometric transition. We construct compact examples admitting the key properties to realize flux supersymmetry breaking and U(1) mediation. Their toric realization allows us to analyze the geometry of curve classes and confirm the topological connection between the hidden and visible sector.

U(1) Mediation of Flux Supersymmetry Breaking

TL;DR

This work demonstrates how a light vector multiplet, arising from RR sector modes in Type IIB string theory, can mediate SUSY breaking between a hidden flux sector and a visible D-brane sector in non-Kähler compactifications. The mediation mechanism relies on St"uckelberg couplings and a careful topological linking of hidden and visible cycles via non-Kähler resolutions, orientifolds, and geometric transitions. The authors develop a detailed four-dimensional effective action, including complex-structure and non-K"ahler moduli, D-terms, and flux-induced superpotentials, and they construct explicit compact geometries (with del Pezzo surfaces and ADE singularities) that realize the desired mediation. They also show how toric techniques and Lie-algebraic data control the global connections between sectors, enabling concrete model-building prospects in string phenomenology and offering a framework to study scale and sequestering effects in SUSY-breaking scenarios.

Abstract

We study the mediation of supersymmetry breaking triggered by background fluxes in Type II string compactifications with N=1 supersymmetry. The mediation arises due to an U(1) vector multiplet coupling to both a hidden supersymmetry breaking flux sector and a visible D-brane sector. The required internal manifolds can be constructed by non-Kaehler resolutions of singular Calabi-Yau manifolds. The effective action encoding the U(1) coupling is then determined in terms of the global topological properties of the internal space. We investigate suitable local geometries for the hidden and visible sector in detail. This includes a systematic study of orientifold symmetries of del Pezzo surfaces realized in compact geometries after geometric transition. We construct compact examples admitting the key properties to realize flux supersymmetry breaking and U(1) mediation. Their toric realization allows us to analyze the geometry of curve classes and confirm the topological connection between the hidden and visible sector.

Paper Structure

This paper contains 34 sections, 117 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. $U(1)$ Mediation of Supersymmetry Breaking
  3. The mediation mechanism and its phenomenology
  4. Hypercharged anomaly mediation
  5. Mediation by an additional $U(1)'$
  6. An embedding into string theory
  7. Mixing hidden and visible $U(1)$ vector multiplets
  8. Outline of the scenario
  9. $U(1)$ Mediation in Non-Kähler Compactifications
  10. Non-Kähler resolutions
  11. The effective action of non-Kähler orientifolds
  12. The complex structure sector
  13. The non-Kähler sector
  14. The scalar potential
  15. The visible sector on D-branes
  16. ...and 19 more sections

Figures (4)

  • Figure 1: Compact manifold with hidden and visible sector singularity.
  • Figure 2: Non-Calabi-Yau space with two local geometries. The three-dimensional chain $\mathcal{B}$ reaching through the orientifold bulk has a two-dimensional boundary $\Sigma=\partial \mathcal{B}$ in the visible MSSM sector on a four-cycle $S$. The four-dimensional chain $\tilde{\Sigma}$ reaching through the bulk has a three-dimensional boundary $\mathcal{A} = \partial \tilde{\Sigma}$ in the hidden flux geometry.
  • Figure 3: Divisor $\tilde{\Sigma}$ with three nodes $p,p',q$.
  • Figure 4: Divisor $\tilde{\Sigma}$ with boundary $\mathcal{A}+\mathcal{A}'$ and the three-chains $\mathcal{B},\mathcal{B}'$ with boundary $\Sigma$.