Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gauge theories on compact toric manifolds   We compute the ${\cal N}=2$ supersymmetric partition function of a gauge
theory on a four-dimensional compact toric manifold via equivariant
localization. The result is given by a piecewise constant function of the
K\"ahler form with jumps along the walls where the gauge symmetry gets
enhanced. The partition function on such manifolds is written as a sum over the
residues of a product of partition functions on $\mathbb{C}^2$. The evaluation
of these residues is greatly simplified by using an "abstruse duality" that
relates the residues at the poles of the one-loop and instanton parts of the
$\mathbb{C}^2$ partition function. As particular cases, our formulae compute
the $SU(2)$ and $SU(3)$ {\it equivariant} Donaldson invariants of
$\mathbb{P}^2$ and $\mathbb{F}_n$ and in the non-equivariant limit reproduce
the results obtained via wall-crossing and blow up methods in the $SU(2)$ case.
Finally, we show that the $U(1)$ self-dual connections induce an anomalous
dependence on the gauge coupling, which turns out to satisfy a $\mathcal{N}=2$
analog of the $\mathcal{N}=4$ holomorphic anomaly equations.

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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th