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Instanton partition functions in \( \mathcal{N} = 2 \) SU(N) gauge theories with a general surface operator, and their \( \mathcal{W} \)-algebra duals

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Abstract

We write down an explicit conjecture for the instanton partition functions in 4d \( \mathcal{N} = 2 \) SU(N) gauge theories in the presence of a certain type of surface operator. These surface operators are classified by partitions of N , and for each partition there is an associated partition function. For the partition N = N we recover the Nekrasov formalism, and when N = 1 + … + 1 we reproduce the result of Feigin et. al. For the case N = 1 + (N − 1) our expression is consistent with an alternative formulation in terms of a restricted SU(N) × SU(N) instanton partition function. When N = 1 + … + 1 + 2 the partition functions can also be obtained perturbatively from certain \( \mathcal{W} \)-algebras known as quasi-superconformal algebras, in agreement with a recent general proposal.

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  1. Niclas Wyllard
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ArXiv ePrint: 1012.1355

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Wyllard, N. Instanton partition functions in \( \mathcal{N} = 2 \) SU(N) gauge theories with a general surface operator, and their \( \mathcal{W} \)-algebra duals. J. High Energ. Phys. 2011, 114 (2011). https://doi.org/10.1007/JHEP02(2011)114

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