Wild wall crossing and BPS giants

2013/05/23 by Dmitry Galakhov, Pietro Longhi, Tom Mainiero +2 · 2 citations
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Charge (physics) #Computation #Coulomb #Electron #Exponential function #Exponential growth #Field (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Quiver #Spectrum (functional analysis) #Supersymmetry #Theoretical physics #hep-th

paper · pdf · doi:10.1007/jhep11(2013)046

105 pages, 25 figures

arxiv created 2013/05/23 · openalex publication_date 2013/11/01 · arxiv updated 2015/06/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We show that the BPS spectrum of pure SU(3) four-dimensional super Yang-Mills with N=2 supersymmetry exhibits a surprising phenomenon: there are regions of the Coulomb branch where the growth of the BPS degeneracies with the charge is exponential. We show this using spectral networks and independently using wall-crossing formulae and quiver methods. The computations using spectral networks provide a very nontrivial example of how these networks determine the four-dimensional BPS spectrum. We comment on some physical implications of the wild spectrum: for example, exponentially many field-theoretic BPS states with large charge are gigantic. Finally, we exhibit some surprising, thus far unexplained, regularities of the BPS spectrum.

Citations

• Crossing the Wall: Branes vs. Bundles
• Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
• On the Spatial Structure of Monopoles
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• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
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• Wall-crossing, Hitchin Systems, and the WKB Approximation
• Moduli spaces of local systems and higher Teichmuller theory
• Thermal monopoles

Cited by

• Elliptic Genera and 3d Gravity
• Multi-cover skeins, quivers, and 3d N = 2 dualities