Quantum Quivers and Hall/Hole Halos

Abstract

Two pictures of BPS bound states in Calabi-Yau compactifications of type II string theory exist, one as a set of particles at equilibrium separations from each other, the other as a fusion of D-branes at a single point of space. We show how quiver quantum mechanics smoothly interpolates between the two, and use this, together with recent mathematical results on the cohomology of quiver varieties, to solve some nontrivial ground state counting problems in multi-particle quantum mechanics, including one arising in the setup of the spherical quantum Hall effect, and to count ground state degeneracies of certain dyons in supersymmetric Yang-Mills theories. A crucial ingredient is a non-renormalization theorem in N=4 quantum mechanics for the first order part of the Lagrangian in an expansion in powers of velocity.

39 pages, 10 figures. v2: minor errors corrected and some parts rewritten for clarity. v3: references added

References in corpus (8)

• Derived Categories and Zero-Brane Stability
• D-Brane Stability and Monodromy
• Split attractor flows and the spectrum of BPS D-branes on the Quintic
• String Webs from Field Theory
• D-brane Dynamics and the Quantum Hall Effect
• D-branes in Massive IIA and Solitons in Chern-Simons Theory
• Graded Lagrangians, exotic topological D-branes and enhanced triangulated categories
• Variations on stability

Cited by in corpus (184)

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• Wall-Crossing from Boltzmann Black Hole Halos
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• Magnetic Monopole Dynamics, Supersymmetry, and Duality
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• Disordered Quivers and Cold Horizons
• Non-BPS Black Rings and Black Holes in Taub-NUT
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• Microstates of the D1-D5-KK System
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• Integrability of Black Hole Orbits in Maximal Supergravity
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• From Black Holes to Quivers
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• Ads(3)/CFT(2) to Ads(2)/CFT(1)
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• Spectral Flow, and the Spectrum of Multi-Center Solutions
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• Marginal Deformations and Rotating Horizons
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• Bolting Multicenter Solutions
• The Cheshire Cap
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• Hair in the Back of a Throat: Non-Supersymmetric Multi-Center Solutions from Kähler Manifolds
• The Geometric Phase in Supersymmetric Quantum Mechanics
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
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• The Coulomb Branch Formula for Quiver Moduli Spaces
• Line defects and (framed) BPS quivers
• Exact Results in Quiver Quantum Mechanics and BPS Bound State Counting
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• Mini-BFSS in Silico
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• A twist on multicenter AdS${}_2$ solutions
• More Bubbling Solutions
• Pure-Higgs states from the Lefschetz-Sommese theorem
• Elliptic genera from multi-centers
• Stability of BPS States and Weak Coupling Limits
• On the Stability of Non-Supersymmetric Quantum Attractors in String Theory
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• Bubbling solutions, entropy enhancement and the fuzzball proposal
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• The Weak Gravity Conjecture and BPS Particles
• Lost Chapters in CHL Black Holes: Untwisted Quarter-BPS Dyons in the ${\mathbb{Z}}_2$ Model
• Attractors with Large Complex Structure for One-Parameter Families of Calabi-Yau Manifolds
• An extremal black hole with a unique ground state
• M5-brane prongs, string soliton bound states and wall-crossing
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• Black Ring Deconstruction
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• Quiver Structure of Heterotic Moduli
• Center Symmetry Breaking in Calabi--Yau Compactifications
• Macdonald Index From Refined Kontsevich-Soibelman Operator
• Instability of Near-Extremal Black Holes in N=2, d=4 Supergravity
• Novel wall-crossing behaviour in rank one $\mathcal{N}=2^{\ast }$ gauge theory
• A Black Hole Levitron