Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multi-centered black holes, scaling solutions and pure-Higgs indices
  from localization   The Coulomb Branch Formula conjecturally expresses the refined Witten index
for $N=4$ Quiver Quantum Mechanics as a sum over multi-centered collinear black
hole solutions, weighted by so-called `single-centered' or `pure-Higgs'
indices, and suitably modified when the quiver has oriented cycles. On the
other hand, localization expresses the same index as an integral over the
complexified Cartan torus and auxiliary fields, which by Stokes' theorem leads
to the famous Jeffrey-Kirwan residue formula. Here, by evaluating the same
integral using steepest descent methods, we show the index is in fact given by
a sum over deformed multi-centered collinear solutions, which encompasses both
regular and scaling collinear solutions. As a result, we confirm the Coulomb
Branch Formula for Abelian quivers in the presence of oriented cycles, and
identify the origin of the pure-Higgs and minimal modification terms as coming
from collinear scaling solutions. For cyclic Abelian quivers, we observe that
part of the scaling contributions reproduce the stacky invariants for trivial
stability, a mathematically well-defined notion whose physics significance had
remained obscure.

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The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
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The categories of this paper are: ao-sci
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga