Circling the Square: Deforming fractional D-branes in Type II/$\Omega \mathcal{R}$ orientifolds

Abstract

We study complex structure deformations of special Lagrangian cycles associated to fractional D-branes at ${\mathbb{Z}}_2$ singularities in Type II/$\Omega \mathcal{R}$ orientifold models. By means of solving hypersurface constraints, we show how to compute the volumes of the most simple D-brane configurations. These volumes are given as a function of the deformation parameters depending on the D-brane position relative to the smoothed out singularity. We observe which cycles keep the special Lagrangian property in various deformation scenarios and what orientifold involutions are allowed. As expected, the volume and thus the tree level value of the gauge coupling hardly change for D-branes not wrapping the exceptional cycle on the deformed singularity, whereas the volume of D-branes passing through the singularity depends on the deformation parameter by some power law.

arXiv comment52 pages, 11 figures, 13 tables; minor clarifications, typos corrected, accepted by JHEP

References in corpus (51)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Consistency Conditions for Orientifolds and D-Manifolds
• Spacetime Instanton Corrections in 4D String Vacua - The Seesaw Mechanism for D-Brane Models
• A SUSY SU(5) Grand Unified Model of Tri-Bimaximal Mixing from A4
• Intersecting Brane Worlds
• The effective action of Type IIA Calabi-Yau orientifolds
• Neutrino Majorana Masses from String Theory Instanton Effects
• D-brane Instantons in Type II String Theory
• Toroidal Compactification Without Vector Structure
• K3 Surfaces and String Duality
• Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
• Type I Strings with F- and B-Flux
• Comments on Open-String Orbifolds with a Non-Vanishing B_{ab}
• On Orbifolds with Discrete Torsion
• Supersymmetric Intersecting Branes on the Type IIA T^6/Z_4 orientifold
• Computation of D-brane instanton induced superpotential couplings - Majorana masses from string theory
• Getting just the Supersymmetric Standard Model at Intersecting Branes on the Z6-orientifold
• Chiral D-brane Models with Frozen Open String Moduli
• A Note on Toroidal Compactifications of the Type I Superstring and Other Superstring Vacuum Configurations with 16 Supercharges
• Gauge Unification in Supersymmetric Intersecting Brane Worlds
• Proton Decay in Intersecting D-brane Models
• Lectures on Calabi-Yau and special Lagrangian geometry
• Resolutions of C^n/Z_n Orbifolds, their U(1) Bundles, and Applications to String Model Building
• Millions of Standard Models on Z6-prime?
• Heterotic MSSM on a Resolved Orbifold
• To Tilt or Not To Tilt: Discrete Gauge Symmetries in Global Intersecting D-Brane Models
• Instanton effects in N=1 brane models and the Kahler metric of twisted matter
• Heterotic Z6-II MSSM Orbifolds in Blowup
• Mapping an Island in the Landscape
• Instantons in N=2 magnetized D-brane worlds
• Lectures on special Lagrangian geometry
• Complete Gauge Threshold Corrections for Intersecting Fractional D6-Branes: The Z6 and Z6' Standard Models
• The Importance of Being Rigid: D6-Brane Model Building on T6/Z2xZ6' with Discrete Torsion
• Rigid D6-branes on T6/[Z(2)xZ(2M)xOmegaR] with discrete torsion
• Gauge Thresholds and Kaehler Metrics for Rigid Intersecting D-brane Models
• Towards the supersymmetric standard model from intersecting D6-branes on the Z_6' orientifold
• Kaehler metrics and gauge kinetic functions for intersecting D6-branes on toroidal orbifolds - The complete perturbative story
• Almost the supersymmetric Standard Model from intersecting D6-branes on the Z_6' orientifold
• Chiral N=1 4d Orientifolds with D-branes at Angles
• Statistics of intersecting D-brane models on T^6/Z_6
• Constructing the supersymmetric Standard Model from intersecting D6-branes on the Z_6' orientifold
• Gauged Linear Sigma Models for toroidal orbifold resolutions
• The Geometer's Toolkit to String Compactifications
• Yukawa couplings and masses of non-chiral states for the Standard Model on D6-branes on T6/Z6'
• Oddness from Rigidness
• Twisting K3 x T^2 Orbifolds
• Circling the Square: Deforming fractional D-branes in Type II/$\Omega \mathcal{R}$ orientifolds
• Intersecting D6-branes on the Z_{12}-II orientifold
• Towards the field theory of the Standard Model on fractional D6-branes on T6/Z6': Yukawa couplings and masses
• Stabilising the supersymmetric Standard Model on the Z_6' orientifold
• D6-Brane Model Building and Discrete Symmetries on T6/Z(2)xZ(6')xOR with Discrete Torsion

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• From Type II string theory towards BSM/dark sector physics
• Towards Geometric D6-Brane Model Building on non-Factorisable Toroidal ${\mathbb{Z}}_4$-Orbifolds
• Deformations, Moduli Stabilisation and Gauge Couplings at One-Loop
• Deforming D-brane models on $T^6/({\mathbb{Z}}_2\times {\mathbb{Z}}_{2M})$ orbifolds
• From Stringy Particle Physics to Moduli Stabilisation and Cosmology
• Massless Spectra and Gauge Couplings at One-Loop on Non-Factorisable Toroidal Orientifolds