Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vafa-Witten invariants from exceptional collections   Supersymmetric D-branes supported on the complex two-dimensional base $S$ of
the local Calabi-Yau threefold $K_S$ are described by semi-stable coherent
sheaves on $S$. Under suitable conditions, the BPS indices counting these
objects (known as generalized Donaldson-Thomas invariants) coincide with the
Vafa-Witten invariants of $S$ (which encode the Betti numbers of the moduli
space of semi-stable sheaves). For surfaces which admit a strong collection of
exceptional sheaves, we develop a general method for computing these invariants
by exploiting the isomorphism between the derived category of coherent sheaves
and the derived category of representations of a suitable quiver with potential
$(Q,W)$ constructed from the exceptional collection. We spell out the
dictionary between the Chern class $\gamma$ and polarization $J$ on $S$ vs. the
dimension vector $\vec N$ and stability parameters $\vec\zeta$ on the quiver
side. For all examples that we consider, which include all del Pezzo and
Hirzebruch surfaces, we find that the BPS indices $\Omega_\star(\gamma)$ at the
attractor point (or self-stability condition) vanish, except for dimension
vectors corresponding to simple representations and pure D0-branes. This opens
up the possibility to compute the BPS indices in any chamber using either the
flow tree or the Coulomb branch formula. In all cases we find precise agreement
with independent computations of Vafa-Witten invariants based on wall-crossing
and blow-up formulae. This agreement suggests that i) generating functions of
DT invariants for a large class of quivers coming from strong exceptional
collections are mock modular functions of higher depth and ii) non-trivial
single-centered black holes and scaling solutions do not exist quantum
mechanically in such local Calabi-Yau geometries.

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The categories of this paper are: funct-an
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg