Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-06-23
Physics
High Energy Physics
High Energy Physics - Theory
47 pages; v2: references added, typos corrected; v3: a version to appear in Nuclear Physics B
Scientific paper
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.
Maruyoshi Kazunobu
Taki Masato
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