D6-brane Splitting on Type IIA Orientifolds

TL;DR

This work analyzes D6-brane splitting on Type IIA ${\bf Z_2\times Z_2}$ orientifolds to understand how open-string moduli Higgsing reshapes gauge symmetry and chiral content. It establishes a one-to-one correspondence between geometric brane splitting (parallel vs not parallel to O6-planes) and field-theory Higgsing in antisymmetric ($Sp(2N)$) or adjoint ($U(N)$) representations, with explicit breaking chains for 1-, 2-, and 3-torus splits. The authors demonstrate concrete implications for Standard-like spectra, presenting a four-family SUSY model from parallel branes with no SM chiral exotics, a non-supersymmetric three-family construction, and a supersymmetric $Sp(2)_L\times Sp(2)_R$-based model, highlighting the phenomenological potential and constraints of brane-world scenarios. Overall, the paper provides a detailed bridge between geometric D-brane dynamics and low-energy gauge structures, expanding the toolkit for constructing realistic, chiral four-dimensional theories from string theory.

Abstract

We study the open-string moduli of supersymmetric D6-branes, addressing both the string and field theory aspects of D6-brane splitting on Type IIA orientifolds induced by open-string moduli Higgsing (i.e., their obtaining VEVs). Specifically, we focus on the Z_2 x Z_2 orientifolds and address the symmetry breaking pattern for D6-branes parallel with the orientifold 6-planes as well as those positioned at angles. We demonstrate that the string theory results, i.e., D6-brane splitting and relocating in internal space, are in one to one correspondence with the field theory results associated with the Higgsing of moduli in the antisymmetric representation of Sp(2N) gauge symmetry (for branes parallel with orientifold planes) or adjoint representation of U(N) (for branes at general angles). In particular, the moduli Higgsing in the open-string sector results in the change of the gauge structure of D6-branes and thus changes the chiral spectrum and family number as well. As a by-product, we provide the new examples of the supersymmetric Standard-like models with the electroweak sector arising from Sp(2N)_L x Sp(2N)_R gauge symmetry; and one four-family example is free of chiral Standard Model exotics.

Figures (7)

• Figure 1: The locations of O6-planes fixed under the orientifold actions $\Omega R$, $\Omega R \omega$, $\Omega R \theta$, and $\Omega R \omega \theta$ (denoted by bold solid lines) for the case of a six-torus factorized on three rectangular two-tori.
• Figure 2: Two distinct brane configurations (denoted by dash-dotted lines): configuration $a$ and its $\omega$ image in the case of D6-branes being split away from the orientifold plane in one, say, third, two-torus. Bold solid lines denote the orientifold planes.
• Figure 3: Four distinct brane configurations: $a$ and its $\omega$ , $\theta$ and $\theta\, \omega$ images in the case of D6-branes being split away from the orientifold plane in two two-tori directions, say, in the second and third two-torus.
• Figure 4: Four distinct brane configurations: $a$ configuration, its $\omega$ , $\theta$ and $\theta\omega$ images as well as four $\Omega \, R$ (not depicted on the figure) in the case of D6-branes being split away from the orientifold plane in all three two-tori directions.
• Figure 5: The D6-brane configuration (dash-dotted line) wrapping a (supersymmetric) three-cycle invariant under orbifold projection. The second configuration is its orientifold image.