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

Abstract

We write down an explicit conjecture for the instanton partition functions in 4d 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)xSU(N) instanton partition function. When N=1+...+1+2 the partition functions can also be obtained perturbatively from certain W-algebras known as quasi-superconformal algebras, in agreement with a recent general proposal.

arXiv comment20 pages

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Cited by in corpus (29)

• Wild Quiver Gauge Theories
• Instanton counting with a surface operator and the chain-saw quiver
• Surface Defects and Resolvents
• M2-brane surface operators and gauge theory dualities in Toda
• The Superconformal Index of the (2,0) Theory with Defects
• From SO/Sp instantons to W-algebra blocks
• W_3 irregular states and isolated N=2 superconformal field theories
• Holomorphic blocks and the 5d AGT correspondence
• A slow review of the AGT correspondence
• Intersecting Surface Defects and Two-Dimensional CFT
• An M-Theoretic Derivation of a 5d and 6d AGT Correspondence, and Relativistic and Elliptized Integrable Systems
• Intersecting defects in gauge theory, quantum spin chains, and Knizhnik-Zamolodchikov equations
• M-Theoretic Derivations of 4d-2d Dualities: From a Geometric Langlands Duality for Surfaces, to the AGT Correspondence, to Integrable Systems
• On W-algebras and the symmetries of defects of 6d N=(2,0) theory
• N=2 SUSY gauge theories on S^4
• Generalized Whittaker states for instanton counting with fundamental hypermultiplets
• Supergroup - extended super Liouville correspondence
• Supersymmetric Rényi Entropy and Defect Operators
• Modular and duality properties of surface operators in N=2* gauge theories
• Correspondences among CFTs with different W-algebra symmetry
• On complete solution of the quantum Dell system
• Orbifolds, Defects and Sphere Partition Function
• N=2 superconformal blocks and instanton partition functions
• Correspondences between WZNW models and CFTs with W-algebra symmetry
• Surface operators in 5d gauge theories and duality relations
• Affine Laumon spaces and iterated W-algebras
• Spectra of elliptic potentials and supersymmetric gauge theories
• Generalized Toda Theory from Six Dimensions and the Conifold
• Chiral rings for surface operators in 4d and 5d SQCD