Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Modular anomaly equations in N=2* theories and their large-N limit   We propose a modular anomaly equation for the prepotential of the N=2* super
Yang-Mills theory on R^4 with gauge group U(N) in the presence of an
Omega-background. We then study the behaviour of the prepotential in a large-N
limit, in which N goes to infinity with the gauge coupling constant kept fixed.
In this regime instantons are not suppressed. We focus on two representative
choices of gauge theory vacua, where the vacuum expectation values of the
scalar fields are distributed either homogeneously or according to the Wigner
semi-circle law. In both cases we derive an all-instanton exact formula for the
prepotential. As an application, we show that the gauge theory partition
function on S^4 at large N localises around a Wigner distribution for the
vacuum expectation values leading to a very simple expression in which the
instanton contribution becomes independent of the coupling constant.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph