D-Brane Probes of Special Holonomy Manifolds

Abstract

Using D2-brane probes, we study various properties of M-theory on singular, non-compact manifolds of G_2 and Spin(7) holonomy. We derive mirror pairs of N=1 supersymmetric three-dimensional gauge theories, and apply this technique to realize exceptional holonomy manifolds as both Coulomb and Higgs branches of the D2-brane world-volume theory. We derive a ``G_2 quotient construction'' of non-compact manifolds which admit a metric of G_2 holonomy. We further discuss the moduli space of such manifolds, including the structure of geometrical transitions in each case. For completeness, we also include familiar examples of manifolds with SU(3) and Sp(2) holonomy, where some of the new ideas are clarified and tested.

79 pages, Latex

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Cited by in corpus (40)

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• Monopole operators in three-dimensional N=4 SYM and mirror symmetry
• AdS_4/CFT_3 duals from M2-branes at hypersurface singularities and their deformations
• Surface Operators and Separation of Variables
• Intersecting brane solutions in string and M-theory
• Quantum moduli spaces from matrix models
• Curious Aspects of Three-Dimensional $\mathcal{N}=1$ SCFTs
• Matter From G(2) Manifolds
• Mirror Symmetry for $G_2$-Manifolds: Twisted Connected Sums and Dual Tops
• Conifold Transitions and Five-Brane Condensation in M-Theory on Spin(7) Manifolds
• $\mathcal{N}=1$ dualities in 2+1 dimensions
• On Gauge Enhancement and Singular Limits in $G_2$ Compactifications of M-theory
• Intersecting 6-branes from new 7-manifolds with G_2 holonomy
• Reflections on the Matter of 3d $\mathcal{N}=1$ Vacua and Local $Spin(7)$ Compactifications
• Towards Generalized Mirror Symmetry for Twisted Connected Sum $G_2$ Manifolds
• M-theory on `toric' G_2 cones and its type II reduction
• A World-Volume Perspective on the Recombination of Intersecting Branes
• N=1 QED in 2+1 dimensions: Dualities and enhanced symmetries
• Branes and fluxes in special holonomy manifolds and cascading field theories
• D-Brane Probes of G_2 Holonomy Manifolds
• Supercoset CFT's for String Theories on Non-compact Special Holonomy Manifolds
• Singular 7-manifolds with G_2 holonomy and intersecting 6-branes
• G_2 Quivers
• Moduli and Brane Intersections
• Emergent Fermi surfaces, fractionalization and duality in supersymmetric QED
• Holography of D-Brane Reconnection
• Geometric Unification of Higgs Bundle Vacua
• Solving matrix models using holomorphy
• Monopoles and confinement in three dimensions from holography
• M-theory on G_2 manifolds and the method of (p,q) brane webs
• Phases of $\mathcal{N}=1$ Quivers in $2+1$ Dimensions
• Some Open Questions in Quiver Gauge Theory
• New G2 holonomy metrics, D6 branes with inherent U(1)xU(1) isometry and gamma-deformations
• Generalized Euler Index, Holonomy Saddles, and Wall-Crossing
• Intersecting branes from 7-manifolds with G_2 holonomy
• Critical properties of three-dimensional many-flavour QEDs
• $\mathcal{N}=1$ supersymmetric three-dimensional QED in the large-$N_f$ limit and applications to super-graphene