Mirror Symmetry in Generalized Calabi-Yau Compactifications

Abstract

We discuss mirror symmetry in generalized Calabi-Yau compactifications of type II string theories with background NS fluxes. Starting from type IIB compactified on Calabi-Yau threefolds with NS three-form flux we show that the mirror type IIA theory arises from a purely geometrical compactification on a different class of six-manifolds. These mirror manifolds have SU(3) structure and are termed half-flat; they are neither complex nor Ricci-flat and their holonomy group is no longer SU(3). We show that type IIA appropriately compactified on such manifolds gives the correct mirror-symmetric low-energy effective action.

54 pages latex, references added, typos corrected

References in corpus (44)

• CFT's From Calabi-Yau Four-folds
• M Theory, Orientifolds and G-Flux
• Mirror Symmetry is T-Duality
• Supersymmetry Breaking and alpha'-Corrections to Flux Induced Potentials
• Superstrings and Topological Strings at Large N
• N=2 Supergravity and N=2 Super Yang-Mills Theory on General Scalar Manifolds: Symplectic Covariance, Gaugings and the Momentum Map
• Two-Dimensional Black Hole and Singularities of CY Manifolds
• New Vacua for Type II String Theory
• RR Flux on Calabi-Yau and Partial Supersymmetry Breaking
• New Formulations of D=10 Supersymmetry and D8-O8 Domain Walls
• On the Vacuum Structure of Type II String Compactifications on Calabi-Yau Spaces with H-Fluxes
• An M-theory Flop as a Large N Duality
• The O(dd) Story of Massive Supergravity
• Orientifolds of K3 and Calabi-Yau Manifolds with Intersecting D-branes
• Solitons, Superpotentials and Calibrations
• Self-Duality, Ramond-Ramond Fields, and K-Theory
• The Symplectic Structure of N=2 Supergravity and its Central Extension
• Type II Theories Compactified on Calabi-Yau Threefolds in the Presence of Background Fluxes
• Fivebranes Wrapped on SLAG Three-Cycles and Related Geometry
• Compactifications of Type IIB Strings to Four Dimensions with Non-trivial Classical Potential
• On Orbifolds with Discrete Torsion
• On Supersymmetry Breaking in String Theory and its Realization in Brane Worlds
• Fibre Bundles and Generalised Dimensional Reduction
• Supergravity couplings: a geometric formulation
• Vanishing Theorems and String Backgrounds
• Type IIB supergravity compactified on a Calabi-Yau manifold with H-fluxes
• Compactification of Type IIB String Theory on Calabi-Yau Threefolds
• A no-go theorem for string warped compactifications
• Massive String Theories From M-Theory and F-Theory
• Kaluza-Klein bundles and manifolds of exceptional holonomy
• Fluxes in Heterotic and Type II String Compactifications
• The 3-Form Multiplet in Supergravity
• N=1 No-Scale Supergravity from IIB Orientifolds
• Curved BPS domain wall solutions in four-dimensional N=2 supergravity
• Fluxes and Branes in Type II Vacua and M-theory Geometry with G(2) and Spin(7) Holonomy
• Massive Type IIA Theory on K3
• Poisson geometry of sigma models with extended supersymmetry
• Heterotic String Theory with Background Fluxes
• IIA String Theory on Calabi-Yau Fourfolds with Background Fluxes
• Calabi-Yau Compactification of Type-IIB string and a Mass Formula of the Extreme Black Holes
• Domain Walls, Black Holes, and Supersymmetric Quantum Mechanics
• Massive Dualities in Six Dimensions
• Massive T-duality in six dimensions
• Romans type IIA theory and the heterotic strings

Cited by in corpus (231)

• Four-dimensional String Compactifications with D-Branes, Orientifolds and Fluxes
• Flux Compactification
• Flux compactifications in string theory: a comprehensive review
• Toward Realistic Intersecting D-Brane Models
• A Geometry for Non-Geometric String Backgrounds
• Moduli Stabilization from Fluxes in a Simple IIB Orientifold
• Nongeometric Flux Compactifications
• Building a Better Racetrack
• New Supersymmetric String Compactifications
• Type IIA Moduli Stabilization
• Generalised Geometry for M-Theory
• Counting Flux Vacua
• Superstrings with Intrinsic Torsion
• The Geometry of D=11 Killing Spinors
• Generalized structures of N=1 vacua
• Supersymmetric Backgrounds from Generalized Calabi-Yau Manifolds
• The effective action of Type IIA Calabi-Yau orientifolds
• Supersymmetric AdS_5 solutions of M-theory
• Stability of flux compactifications and the pattern of supersymmetry breaking
• Fluxes, moduli fixing and MSSM-like vacua in a simple IIA orientifold
• N=1 effective potential from dual type-IIA D6/O6 orientifolds with general fluxes
• A scan for new N=1 vacua on twisted tori
• Supersymmetric AdS(4) compactifications of IIA supergravity
• All supersymmetric solutions of minimal supergravity in six dimensions
• Hitchin Functionals in N=2 Supergravity
• Chiral 4d string vacua with D-branes and NSNS and RR fluxes
• Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure
• More Dual Fluxes and Moduli Fixing
• Progress in D-brane model building
• A ten-dimensional action for non-geometric fluxes
• Compactifications of Heterotic Theory on Non-Kahler Complex Manifolds: I
• T-Duality: Topology Change from H-flux
• SU(3) x SU(3) compactification and mirror duals of magnetic fluxes
• On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs
• From ten to four and back again: how to generalize the geometry
• D-branes on general N=1 backgrounds: superpotentials and D-terms
• Generalized N=1 Orientifold Compactifications and the Hitchin functionals
• Supersymmetric D-branes and calibrations on general N=1 backgrounds
• Compactification with Flux on K3 and Tori
• G-Structures, Fluxes and Calibrations in M-Theory
• Lectures on Generalized Complex Geometry for Physicists
• Generalized Flux Vacua
• The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets
• Mirror symmetric SU(3)-structure manifolds with NS fluxes
• Magnetic charges in local field theory
• General N = 1 Supersymmetric Flux Vacua of (Massive) Type IIA String Theory
• Heterotic Moduli Stabilization with Fractional Chern-Simons Invariants
• Heterotic on Half-flat
• Gauged Supergravities
• General N = 1 Supersymmetric Fluxes in Massive Type IIA String Theory
• The Geometry of D=11 Null Killing Spinors
• Non-Geometric Fluxes in Supergravity and Double Field Theory
• S-duality and Topological Strings
• On the Cosmology of Type IIA Compactifications on SU(3)-structure Manifolds
• Smeared versus localised sources in flux compactifications
• On the Topology and Flux of T-Dual Manifolds
• On the Taxonomy of Flux Vacua
• An Open String Landscape
• Generalised geometry for string corrections
• RR photons
• Effective action of (massive) IIA on manifolds with SU(3) structure
• Lectures on Nongeometric Flux Compactifications
• Fixing Moduli in Exact Type IIA Flux Vacua
• Massive Abelian Gauge Symmetries and Fluxes in F-theory
• Exploiting N=2 in consistent coset reductions of type IIA
• Statistics of M theory Vacua
• Supersymmetric M-theory compactifications with fluxes on seven-manifolds and G-structures
• Generalized complex manifolds and supersymmetry
• Towards Minkowski Vacua in Type II String Compactifications
• N=1 geometries for M-theory and type IIA strings with fluxes
• New string vacua from twistor spaces
• SUSY Breaking and Moduli Stabilization from Fluxes in Gauged 6D Supergravity
• Scherk-Schwarz reduction of M-theory on G2-manifolds with fluxes
• On supersymmetric solutions of type IIB supergravity with general fluxes
• Non-Perturbative Superpotentials in F-theory and String Duality
• Moduli Stabilisation in Heterotic String Compactifications
• Geometric Transitions, Flops and Non-Kahler Manifolds: I
• Effective actions and N=1 vacuum conditions from SU(3) x SU(3) compactifications
• The effective action of type II Calabi-Yau orientifolds
• Gauging the Heisenberg algebra of special quaternionic manifolds
• Branes on Generalized Calibrated Submanifolds
• Local string models of soft supersymmetry breaking
• D-branes in Nongeometric Backgrounds
• Topological mirror symmetry with fluxes
• Geometric Transitions, Flops and Non-Kahler Manifolds: II
• The Hitchin functionals and the topological B-model at one loop
• The Scherk-Schwarz mechanism as a flux compactification with internal torsion
• All homogeneous N=2 M-theory truncations with supersymmetric AdS4 vacua
• E7(7) formulation of N=2 backgrounds
• In the Realm of the Geometric Transitions
• Fluxes in M-theory on 7-manifolds and G structures
• AdS Strings with Torsion: Non-complex Heterotic Compactifications
• M-theory Compactifications on Manifolds with G2 Structure
• Type II Strings and Generalized Calabi-Yau Manifolds
• Nearly Kaehler Reduction
• T-duality with H-flux: non-commutativity, T-folds and G x G structure
• Spontaneous N=2 to N=1 Supersymmetry Breaking in Supergravity and Type II String Theory
• An Orientifold with Fluxes and Branes via T-duality
• The Type IIA Flux Potential, 4-forms and Freed-Witten anomalies
• Heterotic String Compactifications on Half-flat Manifolds II
• D6-branes and torsion
• A sigma model field theoretic realization of Hitchin's generalized complex geometry
• Membrane Instantons and de Sitter Vacua
• Challenge for spontaneous CP violation in Type IIB orientifolds with fluxes
• Fluxes in M-theory on 7-manifolds: G-structures and Superpotential
• String instantons, fluxes and moduli stabilization
• Nongeometry, Duality Twists, and the Worldsheet
• SU(3)-instantons and $G_2,Spin(7)$-heterotic string solitons
• General Type IIB Fluxes with SU(3) Structures
• G-structures and Flavouring non-Abelian T-duality
• Towards reduction of type II theories on SU(3) structure manifolds
• M-theory compactification, fluxes and AdS_4
• Classification of Supersymmetric Flux Vacua in M Theory
• Heterotic compactifications and nearly-Kahler manifolds
• Bundles over Nearly-Kahler Homogeneous Spaces in Heterotic String Theory
• M-theory on seven-dimensional manifolds with SU(3) structure
• Area metric gravity and accelerating cosmology
• Supersymmetric Intersecting D6-branes and Fluxes in Massive Type IIA String Theory
• Low Energy Supersymmetry from Non-Geometry
• NS-NS fluxes in Hitchin's generalized geometry
• Conifolds and Geometric Transitions
• Geometry of manifolds with area metric: multi-metric backgrounds
• Fermions on the Anti-Brane: Higher Order Interactions and Spontaneously Broken Supersymmetry
• D-brane instantons and the effective field theory of flux compactifications
• Gauge-Gravity Dualities, Dipoles and New Non-Kahler Manifolds
• The N=1 Low-Energy Effective Action of Spontaneously Broken N=2 Supergravities
• 1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetry
• Calabi-Yau Duals of Torus Orientifolds
• Domain walls from ten dimensions
• A special road to AdS vacua
• Supersymmetric Vacua in N=2 Supergravity
• Reducing democratic type II supergravity on SU(3) x SU(3) structures
• G-structures and Domain Walls in Heterotic Theories
• Generalised discrete torsion and mirror symmetry for G_2 manifolds
• Superstring Orientifolds with Torsion: O5 Orientifolds of Torus Fibrations and their Massless Spectra
• Hermitian-Yang-Mills equations and pseudo-holomorphic bundles on nearly Kaehler and nearly Calabi-Yau twistor 6-manifolds
• Flux Vacua Statistics for Two-Parameter Calabi-Yau's
• Heterotic-type IIA duality with fluxes
• Supersymmetric completion of M-theory 4D-gauge algebra from twisted tori and fluxes
• Scalar potential for the gauged Heisenberg algebra and a non-polynomial antisymmetric tensor theory
• Moduli Stabilising in Heterotic Nearly Kähler Compactifications
• On The Warped Heterotic Axion
• String vacua with flux from freely-acting obifolds
• Heterotic domain wall solutions and SU(3) structure manifolds
• D-terms on the resolved conifold
• Non-Kaehler attracting manifolds
• Domain Walls, Hitchin's Flow Equations and G_2-Manifolds
• Non-geometric fluxes as supergravity backgrounds
• Laplacian spectrum on a nilmanifold, truncations and effective theories
• On Aspects of Holographic Thermal QCD at Finite Coupling
• Warped Wilson Line DBI Inflation
• No-scale supersymmetry breaking vacua and soft terms with torsion
• Modified pure spinors and mirror symmetry
• Heterotic backgrounds via generalised geometry: moment maps and moduli
• Structures in the Gauge/Gravity Duality Cascade
• Brane Inflation and Moduli Stabilization on Twisted Tori
• Seeing through the String Landscape - a String Hunter's Companion in Particle Physics and Cosmology
• Complex/Symplectic Mirrors
• Half-flat structures on products of three-dimensional Lie groups
• Curvatures and potential of M-theory in D=4 with fluxes and twist
• Dipole-Deformed Bound States and Heterotic Kodaira Surfaces
• M5-brane geometries, T-duality and fluxes
• Non-perturbative vacua for M-theory on G2 manifolds
• Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
• A landscape of non-supersymmetric AdS vacua on coset manifolds
• N=1 domain wall solutions of massive type II supergravity as generalized geometries
• Time reversal and $\mathbf{CP}$ invariance in Calabi-Yau compactifications
• On T-folds, G-structures and Supersymmetry
• $\mathcal{N}=(1,1)$ supersymmetric AdS${}_3$ in 10 dimensions
• Twisted tori and fluxes: a no go theorem for Lie groups of weak G_2 holonomy
• Real symplectic formulation of local special geometry
• Warped generalized geometry compactifications, effective theories and non-perturbative effects
• Uplifting the Iwasawa
• Pure spinor equations to lift gauged supergravity
• The Kahler Cone as Cosmic Censor
• The Ricci Curvature of Half-flat Manifolds
• Delocalized SYZ Mirrors and Confronting Top-Down $SU(3)$-Structure Holographic Meson Masses at Finite $g$ and $N_c$ with P(article) D(ata) G(roup) Values
• Geometric Transitions on non-Kaehler Manifolds
• The N=4 effective action of type IIA supergravity compactified on SU(2)-structure manifolds
• Enhanced supersymmetry from vanishing Euler number
• Classifying Supergravity Solutions
• Type IIA orientifold compactification on SU(2)-structure manifolds
• Topology and Flux of T-Dual Manifolds with Circle Actions
• Five dimensional 2-branes from special Lagrangian wrapped M5-branes
• Black hole entropy and topological strings on generalized CY manifolds
• Topological Strings on Non-Commutative Resolutions
• Gauged supergravities and their symmetry-breaking vacua in F-theory
• On topological F-theory
• Freed-Witten anomaly in general flux compactification
• Domain wall flow equations and SU(3)xSU(3) structure compactifications
• Type IIA Killing spinors and calibrations
• Non-Kahler Resolved Conifold, Localized Fluxes in M-Theory and Supersymmetry
• From wrapped M-branes to Calabi-Yau black holes and strings
• On Missing Bianchi Identities in Cohomology Formulation
• Heterotic Moduli Stabilisation and Non-Supersymmetric Vacua
• Moduli Stabilisation in Heterotic Models with Standard Embedding
• Quantum Corrections in String Compactifications on SU(3) Structure Geometries
• Knot Invariants and M-Theory I: Hitchin Equations, Chern-Simons Actions, and the Surface Operators
• SU(3)-structures on submanifolds of a Spin(7)-manifold
• Electric-Magnetic Dualities in Non-Abelian and Non-Commutative Gauge Theories
• Galilean type IIA backgrounds and a map
• Topological A-Type Models with Flux
• Fixing moduli in exact Type IIA flux vacua
• Left-invariant Einstein metrics on $S^3\times S^3$
• Classification of Shift-Symmetric No-Scale Supergravities
• Type IIB Flows with N=1 Supersymmetry
• F-Theory, Seiberg-Witten Curves and N = 2 Dualities
• Flow Equations for Uplifting Half-Flat to Spin(7) Manifolds
• A Note on Mirror Symmetry for Manifolds with Spin(7) Holonomy
• T-duality of singular spacetime compactifications in an H-flux
• On the Scalar Spectrum of the Y^{p,q} Manifolds
• A Note on Fluxes in Six-Dimensional String Theory Backgrounds
• Global aspects of the renormalization group and the Hierarchy problem
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• Fluxes, moduli fixing and MSSM-like vacua in Type IIA String Theory
• Consistent truncation with dilatino condensation on nearly Kähler and Calabi-Yau manifolds
• Gauged supergravities from M-theory reductions
• Half-flat Quantum Hair
• Geometric Transitions, Non-Kahler Geometries and String Vacua
• Heterotic type IIA duality with fluxes - towards the complete story
• Generalized Geometry and Partial Supersymmetry Breaking
• Flux-induced isometry gauging in heterotic strings
• Dimensional Reductions of DFT and Mirror Symmetry for Calabi-Yau Three-folds and $K3\times T^2$
• Nearly-Kaehler dimensional reduction of the heterotic string
• On the Geometry of Coset Models with Flux
• A Massive S-duality in 4 dimensions
• SU(3)_c X SU(4)_L X U(1)_x model for three families
• Eight-dimensional non-geometric heterotic strings and enhanced gauge groups
• Stabilization of moduli by fluxes
• Minkowski vacuum transitions in (non-geometric) flux compactifications
• N=1 domain wall solutions of massive type II supergravity and the issue of mirror symmetry