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

By H. Kanno, Yuji Tachikawa. 2011

156 citations recorded by the source corpus.

We describe the moduli space of SU(N) instantons in the presence of a general surface operator of type N = n1 + ⋯ + nM 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 nI 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 nI. By explicit calculations, we check that the partition function agrees with the norm of a coherent state in the corresponding Verma module.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/01ca5e3c5515703b1ed19061624bd72f24110674

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Citations in the corpus

Defects and quantum Seiberg-Witten geometry (2014, methodology): “This computation is performed by treating the surface defect as a monodromy defect and applying the orbifolding procedure introduced in [15, 16].”
Nilpotent orbits and codimension-two defects of 6d N=(2,0) theories (2012, result): “This proposal has been checked to some extent by recent works [34, 35, 36].”