Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $R^3$ index for four-dimensional $N=2$ field theories   In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay
across walls of marginal stability in the space of Coulomb branch parameters,
leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a
supersymmetric index $I$ which receives contributions from 1/2-BPS states,
generalizing the familiar Witten index $Tr (-1)^F e^{-\beta H}$. We expect $I$
to be smooth away from loci where massless particles appear, thanks to
contributions from the continuum of multi-particle states. Taking inspiration
from a similar phenomenon in the hypermultiplet moduli space of $N=2$ string
vacua, we conjecture a formula expressing $I$ in terms of the BPS indices
$\Omega(\gamma,u)$, which is continuous across the walls and exhibits the
expected contributions from single particle states at large $\beta$. This gives
a universal prediction for the contributions of multi-particle states to the
index $I$. This index is naturally a function on the moduli space after
reduction on a circle, closely related to the canonical hyperk\"ahler metric
and hyperholomorphic connection on this space.

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The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn