(Dis)assembling Special Lagrangians

Abstract

We explain microscopically why split attractor flows, known to underlie certain stationary BPS solutions of four dimensional N=2 supergravity, are the relevant data to describe wrapped D-branes in Calabi-Yau compactifications of type II string theory. We work entirely in the context of the classical geometry of A-branes, i.e. special Lagrangian submanifolds, avoiding both the use of homological algebra and explicit constructions of special Lagrangians. Our results provide a way to disassemble and assemble arbitrary special Lagrangians to and from more simple building blocks, giving a concrete way to determine for example marginal stability walls and deformation moduli spaces.

35 pages, 12 figures, v2: references added, expanded discussion

References in corpus (20)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• N=2 Extremal Black Holes
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Gauge Theory and the Excision of Repulson Singularities
• The spectrum of BPS branes on a noncompact Calabi-Yau
• Arithmetic and Attractors
• Classical and quantum N=2 supersymmetric black holes
• Supersymmetric Three-cycles and (Super)symmetry Breaking
• Open string - string junction transitions
• D-branes as Solitons of an N=1, D=10 Non-commutative Gauge Theory
• Constraints on the BPS Spectrum of N = 2, D = 4 Theories with A-D-E Flavor Symmetry
• BPS States on a Three Brane Probe
• The moduli space of special Lagrangian submanifolds
• The BPS Spectrum of N=2 SU(N) SYM and Parton Branes
• String Webs from Field Theory
• The 0-brane action in a general D=4 supergravity background
• Graded Lagrangians, exotic topological D-branes and enhanced triangulated categories
• D-Branes and N=1 Supersymmetry
• Moment maps, monodromy and mirror manifolds
• D-branes and Vector Bundles on Calabi-Yau Manifolds: a view from the Helix

Cited by in corpus (12)

• Black hole bound states in AdS_3 x S^2
• Non-perturbative F-terms across lines of BPS stability
• Attractors and Black Rings
• Bound state transformation walls
• The Attractor Mechanism in Five Dimensions
• D-branes and Azumaya noncommutative geometry: From Polchinski to Grothendieck
• Complex structure moduli stability in toroidal compactifications
• D-branes and Azumaya/matrix noncommutative differential geometry, I: D-branes as fundamental objects in string theory and differentiable maps from Azumaya/matrix manifolds with a fundamental module to real manifolds
• Azumaya noncommutative geometry and D-branes - an origin of the master nature of D-branes
• D-branes of A-type, their deformations, and Morse cobordism of A-branes on Calabi-Yau 3-folds under a split attractor flow: Donaldson/Alexander-Hilden-Lozano-Montesinos-Thurston/Hurwitz/Denef-Joyce meeting Polchinski-Grothendieck
• Distributions of extremal black holes in Calabi-Yau compactifications
• Interpolating between multi-center microstate geometries