Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deformed Prepotential, Quantum Integrable System and Liouville Field
  Theory   We study the dual descriptions recently discovered for the Seiberg-Witten
theory in the presence of surface operators. The Nekrasov partition function
for a four-dimensional N=2 gauge theory with a surface operator is believed
equal to the wave-function of the corresponding integrable system, or the
Hitchin system, and is identified with the conformal block with a degenerate
field via the AGT relation. We verify the conjecture by showing that the null
state condition leads to the Schrodinger equations of the integrable systems.
Furthermore, we show that the deformed prepotential emerging from the period
integrals of the principal function corresponds to monodromy operation of the
conformal block. We also give the instanton partition functions for the
asymptotically free SU(2) gauge theories in the presence of the surface
operator via the AGT relation. We find that these partition functions involve
the counting of two- and four-dimensional instantons.

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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph