Gauge Theoretical Construction of Non-compact Calabi-Yau Manifolds

Abstract

We construct the non-compact Calabi-Yau manifolds interpreted as the complex line bundles over the Hermitian symmetric spaces. These manifolds are the various generalizations of the complex line bundle over CP^{N-1}. Imposing an F-term constraint on the line bundle over CP^{N-1}, we obtain the line bundle over the complex quadric surface Q^{N-2}. On the other hand, when we promote the U(1) gauge symmetry in CP^{N-1} to the non-abelian gauge group U(M), the line bundle over the Grassmann manifold is obtained. We construct the non-compact Calabi-Yau manifolds with isometries of exceptional groups, which we have not discussed in the previous papers. Each of these manifolds contains the resolution parameter which controls the size of the base manifold, and the conical singularity appears when the parameter vanishes.

LaTeX2e, 27 pages, no figures, typos corrected

References in corpus (8)

• Complex geometry of conifolds and 5-brane wrapped on 2-sphere
• Hyper-Kahler Calabi Metrics, L^2 Harmonic Forms, Resolved M2-branes, and AdS_4/CFT_3 Correspondence
• 3-branes on spaces with R x S^2 x S^3 topology
• Supersymmetric Domain Walls from Metrics of Special Holonomy
• CFT Description of String Theory Compactified on Non-compact Manifolds with G_2 Holonomy
• Ricci-flat Kahler Manifolds from Supersymmetric Gauge Theories
• Supersymmetric Nonlinear Sigma Models on Ricci-flat Kahler Manifolds with O(N) Symmetry
• A Note on Conifolds

Cited by in corpus (21)

• Resolutions of C^n/Z_n Orbifolds, their U(1) Bundles, and Applications to String Model Building
• Domain Walls with Non-Abelian Clouds
• On Spin(7) holonomy metric based on SU(3)/U(1): II
• Hyper-Kahler Sigma Models on (Co)tangent Bundles with SO(n) isometry
• SO and USp Kahler and Hyper-Kahler Quotients and Lumps
• Calabi-Yau Manifolds of Cohomogeneity One as Complex Line Bundles
• Conformal Sigma Models with Anomalous Dimensions and Ricci Solitons
• T-duality Transformation of Gauged Linear Sigma Model with F-term
• Auxiliary Field Methods in Supersymmetric Nonlinear Sigma Models
• Higher-curvature generalization of Eguchi-Hanson spaces
• Gauged Linear Sigma Model with F-term for A-type ALE Space
• Non-Abelian Vortex-String Dynamics from Nonlinear Realization
• Construction of Supersymmetric Nonlinear Sigma Models on Noncompact Calabi-Yau Manifolds with Isometry
• Wilsonian Renormalization Group Approach to $\mathcal{N}=2$ Supersymmetric Sigma Models
• Construction of Supergravity Backgrounds with a Dilaton Field
• Fractional black $p$-branes on orbifold ${\mathbb{C}}^n/{\mathbb{Z}}_n$
• Orbifold black holes
• Kahler Potentials on Toric Varieties
• Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties
• Explicit formula of deformation quantization with separation of variables for complex two-dimensional locally symmetric Kähler manifold
• Zero-mode Spectrum of Eleven-dimensional Theory on the Plane-wave Background