Derives the general non-holomorphic completion for arbitrary n-center BPS black hole indices using localization on the refined Witten index in supersymmetric quantum mechanics, yielding generalized error functions from phase space and transverse integrals.
Quantum Black Holes, Wall Crossing, and Mock Modular Forms
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
abstract
We show that the meromorphic Jacobi form that counts the quarter-BPS states in N=4 string theories can be canonically decomposed as a sum of a mock Jacobi form and an Appell-Lerch sum. The quantum degeneracies of single-centered black holes are Fourier coefficients of this mock Jacobi form, while the Appell-Lerch sum captures the degeneracies of multi-centered black holes which decay upon wall-crossing. The completion of the mock Jacobi form restores the modular symmetries expected from $AdS_3/CFT_2$ holography but has a holomorphic anomaly reflecting the non-compactness of the microscopic CFT. For every positive integral value m of the magnetic charge invariant of the black hole, our analysis leads to a special mock Jacobi form of weight two and index m, which we characterize uniquely up to a Jacobi cusp form. This family of special forms and another closely related family of weight-one forms contain almost all the known mock modular forms including the mock theta functions of Ramanujan, the generating function of Hurwitz-Kronecker class numbers, the mock modular forms appearing in the Mathieu and Umbral moonshine, as well as an infinite number of new examples.
representative citing papers
An extended square matrix of (x,q)-series indexed by boundary parabolic SL2(C) flat connections completely describes the resurgent structure, Stokes constants, and Borel transform of Chern-Simons perturbation theory at the trivial flat connection for hyperbolic knot complements.
Constructs topological elliptic genera as G-equivariant refinements of classical elliptic genera and derives a divisibility result for Euler numbers of Sp-manifolds.
Resurgent cyclic orbits' algebraic structure plus the leading q-series term determines the asymptotic growth exponent of dual q-series coefficients, which equals an effective central charge c_eff in a related 3d N=2 QFT.
Mock theta functions admit a unique resurgent continuation across their natural boundary, with the continuation fixed by their Mordell-Appell integrals via rotated Laplace contours.
citing papers explorer
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Black Hole Quantum Mechanics and Generalized Error Functions
Derives the general non-holomorphic completion for arbitrary n-center BPS black hole indices using localization on the refined Witten index in supersymmetric quantum mechanics, yielding generalized error functions from phase space and transverse integrals.
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Resurgence of Chern-Simons theory at the trivial flat connection
An extended square matrix of (x,q)-series indexed by boundary parabolic SL2(C) flat connections completely describes the resurgent structure, Stokes constants, and Borel transform of Chern-Simons perturbation theory at the trivial flat connection for hyperbolic knot complements.
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Topological Elliptic Genera I -- The mathematical foundation
Constructs topological elliptic genera as G-equivariant refinements of classical elliptic genera and derives a divisibility result for Euler numbers of Sp-manifolds.
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$c_{\rm eff}$ from Resurgence at the Stokes Line
Resurgent cyclic orbits' algebraic structure plus the leading q-series term determines the asymptotic growth exponent of dual q-series coefficients, which equals an effective central charge c_eff in a related 3d N=2 QFT.
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On Uniqueness of Mock Theta Functions
Mock theta functions admit a unique resurgent continuation across their natural boundary, with the continuation fixed by their Mordell-Appell integrals via rotated Laplace contours.