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Chiral D-brane Models with Frozen Open String Moduli

Ralph Blumenhagen, Mirjam Cvetic, Fernando Marchesano, Gary Shiu

TL;DR

This paper tackles the persistent problem of open-string moduli in N=1 intersecting D-brane models by engineering rigid D6-branes that wrap 3-cycles with no position or Wilson-line moduli. It achieves this inside a Z2×Z2' orientifold with discrete torsion, enabling the construction of globally consistent, chiral vacua free of adjoint matter and capable of SU(4) asymptotic freedom in a Pati-Salam-like setup. The work then integrates flux compactifications, showing how ISD G3 flux stabilizes complex-structure/dilaton moduli and yields new classes of N=1 and N=0 chiral flux vacua, thus offering a framework for simultaneous open and closed string moduli stabilization. Together, these results provide concrete model-building strategies and explicit examples that move string constructions closer to realistic phenomenology, including potential gaugino condensation and implications for gauge coupling unification. The approach highlights the interplay between rigid open-string sectors and flux-induced stabilization as a path toward more predictive D-brane realizations of beyond-Standard-Model physics.

Abstract

Most intersecting D-brane vacua in the literature contain additional massless adjoint fields in their low energy spectrum. The existence of these additional fields make it difficult to obtain negative beta functions and, eventually, asymptotic freedom. We address this important issue for N=1 intersecting D-brane models, rephrasing the problems in terms of (open string) moduli stabilization. In particular, we consider a Z2 x Z2 orientifold construction where D6-branes wrap rigid 3-cycles and such extra adjoint fields do not arise. We derive the model building rules and consistency conditions for intersecting branes in this background, and provide N=1 chiral vacua free of adjoint fields. More precisely, we construct a Pati-Salam-like model whose SU(4) gauge group is asymptotically free. We also comment on the application of these results for obtaining gaugino condensation in chiral D-brane models. Finally, we embed our constructions in the framework of flux compactification, and construct new classes of N=1 and N=0 chiral flux vacua.

Chiral D-brane Models with Frozen Open String Moduli

TL;DR

This paper tackles the persistent problem of open-string moduli in N=1 intersecting D-brane models by engineering rigid D6-branes that wrap 3-cycles with no position or Wilson-line moduli. It achieves this inside a Z2×Z2' orientifold with discrete torsion, enabling the construction of globally consistent, chiral vacua free of adjoint matter and capable of SU(4) asymptotic freedom in a Pati-Salam-like setup. The work then integrates flux compactifications, showing how ISD G3 flux stabilizes complex-structure/dilaton moduli and yields new classes of N=1 and N=0 chiral flux vacua, thus offering a framework for simultaneous open and closed string moduli stabilization. Together, these results provide concrete model-building strategies and explicit examples that move string constructions closer to realistic phenomenology, including potential gaugino condensation and implications for gauge coupling unification. The approach highlights the interplay between rigid open-string sectors and flux-induced stabilization as a path toward more predictive D-brane realizations of beyond-Standard-Model physics.

Abstract

Most intersecting D-brane vacua in the literature contain additional massless adjoint fields in their low energy spectrum. The existence of these additional fields make it difficult to obtain negative beta functions and, eventually, asymptotic freedom. We address this important issue for N=1 intersecting D-brane models, rephrasing the problems in terms of (open string) moduli stabilization. In particular, we consider a Z2 x Z2 orientifold construction where D6-branes wrap rigid 3-cycles and such extra adjoint fields do not arise. We derive the model building rules and consistency conditions for intersecting branes in this background, and provide N=1 chiral vacua free of adjoint fields. More precisely, we construct a Pati-Salam-like model whose SU(4) gauge group is asymptotically free. We also comment on the application of these results for obtaining gaugino condensation in chiral D-brane models. Finally, we embed our constructions in the framework of flux compactification, and construct new classes of N=1 and N=0 chiral flux vacua.

Paper Structure

This paper contains 23 sections, 65 equations, 4 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Open string moduli for intersecting branes
  3. Open string moduli on Calabi-Yau's
  4. Toroidal orientifolds
  5. Other constructions
  6. Intersecting rigid branes on $\mathbb{Z}_2\times \mathbb{Z}_2'$
  7. The orbifold background
  8. Rigid 3-cycles
  9. Discrete positions and Wilson lines
  10. The orientifold projection
  11. Spectrum
  12. Consistency and supersymmetry conditions
  13. Examples
  14. Model Building strategy
  15. A simple ${\cal N}=1$ D-brane model
  16. ...and 8 more sections

Figures (4)

  • Figure 1: Choices of complex structures on the ${\bf T}^2$ factors and $\mathbb{Z}_2$ fixed points
  • Figure 2: Fractional brane running through 4 fixed points for each twisted sector. Fixed points are denoted by dots in the $\Theta$, by squares in the $\Theta'$ and by crosses in the $\Theta\Theta'$ twisted sector.
  • Figure 3: Two fractional branes with different bulk wrapping numbers and charged under the same set of fixed points.
  • Figure 4: Intersection points of the rigid branes $a_1$ and $a_2$. The numbers on the second and third ${\bf T}^2$ count the eight intersection points.