Symmetry Breaking Bulk Effects in Local D-brane Models
Anshuman Maharana
TL;DR
The paper analyzes how compactification-induced bulk effects break global symmetries in local D-brane models, using ${\mathbb{C}^{3}/ \mathbb{Z}_{3}}$ as a prototype. It shows that symmetry breaking is governed by the lowest-dimension Lichnerowicz zero-modes on cone-like geometries, with SU(3) breaking suppressed by volume-related factors while U(1) breaking is more suppressed, leading to a hierarchical pattern. In the open-string sector, the leading symmetry-breaking Yukawa-like operators arise from flavon representations $(1,1)$, yielding gauge-invariant operators $\lambda^{i}_{j}$ and $\beta^{i}_{j}$ with flavon vevs scaling as ${\cal V}^{-1/3}$. The approach provides a general framework for predicting bulk-to-brane flavor-breaking effects in local models and can be extended to other complex cones and F-theory contexts.
Abstract
We study symmetry breaking effects in local D-brane models that arise as a result of compactification, taking models constructed on C^3/Z_3 as prototype. Zero-modes of the Lichnerowicz operator in cone-like geometries have a power law behaviour; thus the leading symmetry breaking effects are captured by the modes with the lowest scaling dimension which transform non-trivially under the isometry group. Combining this with the fact that global symmetries in local models are gauged upon compactification we determine the strength and form of the leading operators responsible for the symmetry breaking. We find a hierarchical separation in the size of symmetry breaking parameters.