From SO/Sp instantons to W-algebra blocks

Abstract

We study instanton partition functions for N=2 superconformal Sp(1) and SO(4) gauge theories. We find that they agree with the corresponding U(2) instanton partitions functions only after a non-trivial mapping of the microscopic gauge couplings, since the instanton counting involves different renormalization schemes. Geometrically, this mapping relates the Gaiotto curves of the different realizations as double coverings. We then formulate an AGT-type correspondence between Sp(1)/SO(4) instanton partition functions and chiral blocks with an underlying W(2,2)-algebra symmetry. This form of the correspondence eliminates the need to divide out extra U(1) factors. Finally, to check this correspondence for linear quivers, we compute expressions for the Sp(1)-SO(4) half-bifundamental.

83 pages, 29 figures; minor changes

References in corpus (8)

• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Affine SL(2) conformal blocks from 4d gauge theories
• Six-dimensional D_N theory and four-dimensional SO-USp quivers
• Affine sl(N) conformal blocks from N=2 SU(N) gauge theories
• Exotic instanton counting and heterotic/type I' duality
• F-theoretic vs microscopic description of a conformal N=2 SYM theory
• Instanton partition functions in N=2 SU(N) gauge theories with a general surface operator, and their W-algebra duals
• Equivariant volumes of non-compact quotients and instanton counting

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• Hilbert Series for Moduli Spaces of Two Instantons
• Counting Exceptional Instantons
• A slow review of the AGT correspondence
• Towards a 4d/2d correspondence for Sicilian quivers
• Mayer-Cluster Expansion of Instanton Partition Functions and Thermodynamic Bethe Ansatz
• Instantons from Blow-up
• Higgs, Coulomb, and Hall-Littlewood
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• Instanton counting and O-vertex
• More on topological vertex formalism for 5-brane webs with O5-plane
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• Effective gravitational couplings of four-dimensional $\mathcal{N}=2$ supersymmetric gauge theories
• (de)Tails of Toda CFT
• Recursive Method for Nekrasov partition function for classical Lie groups
• Seiberg-Witten geometry of four-dimensional N=2 SO-USp quiver gauge theories, I
• Argyres-Douglas Theories, S-duality and AGT Correspondence
• Bethe/Gauge Correspondence for SO/Sp Gauge Theories and Open Spin Chains
• Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions
• The gravity duals of SO/USp superconformal quivers
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• Orthosymplectic Superinstanton Counting and Brane Dynamics
• Bethe/Gauge Correspondence for $A_N$ Spin Chains with Integrable Boundaries