Instanton counting with a surface operator and the chain-saw quiver

Details Instanton counting with a surface operator and the chain-saw quiver Instanton counting with a surface operator and the chain-saw quiver

2011-05-02

arxiv.org/abs/1105.0357v2

JHEP 06 (2011) 119

Physics

High Energy Physics

High Energy Physics - Theory

25+5 pages, 2 figures, 1 Mathematica file. v2: published version

Scientific paper

10.1007/JHEP06(2011)119

We describe the moduli space of SU(N) instantons in the presence of a general surface operator of type N=n_1+ ... +n_M in terms of the representations of the so-called chain-saw quiver, which allows us to write down the instanton partition function as a summation over the fixed point contributions labeled by Young diagrams. We find that the instanton partition function depends on the ordering of n_I which fixes a choice of the parabolic structure. This is in accord with the fact that the Verma module of the W-algebra also depends on the ordering of n_I. By explicit calculations, we check that the partition function agrees with the norm of a coherent state in the corresponding Verma module.

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