Wall-crossing made smooth

Abstract

In $D=4,N=2$ theories on $R^{3,1}$, the index receives contributions not only from single-particle BPS states, counted by the BPS indices, but also from multi-particle states made of BPS constituents. In a recent work [arXiv:1406.2360], a general formula expressing the index in terms of the BPS indices was proposed, which is smooth across walls of marginal stability and reproduces the expected single-particle contributions. In this note, I analyze the two-particle contributions predicted by this formula, and show agreement with the spectral asymmetry of the continuum of scattering states in the supersymmetric quantum mechanics of two non-relativistic, mutually non-local dyons. This provides a physical justification for the error function profile used in the mathematics literature on indefinite theta series, and in the physics literature on black hole partition functions.

14 pages, 1 figure

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Cited by in corpus (14)

• Multiple D3-instantons and mock modular forms I
• Single-centered black hole microstate degeneracies from instantons in supergravity
• Black holes and higher depth mock modular forms
• More on Homological Supersymmetric Quantum Mechanics
• APS $\eta$-invariant, path integrals, and mock modularity
• Scaling Black Holes and Modularity
• Wall Crossing from Dirac Zeromodes
• An Elliptic Triptych
• Three-Charge Black Holes and Quarter BPS States in Little String Theory
• Mock modularity from black hole scattering states
• Squashed Toric Manifolds and Higher Depth Mock Modular Forms
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Hamiltonian Truncation Study of Supersymmetric Quantum Mechanics: S-Matrix and Metastable States
• Quantum Black Hole Entropy and Localization in Supergravity