### 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.

Original language | English (US) |
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Article number | 53 |

Journal | Journal of High Energy Physics |

Volume | 2011 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 2011 |

Externally published | Yes |

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### Keywords

- Conformal and W symmetry
- M-Theory
- Nonperturbative effects
- Supersymmetric gauge theory

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Journal of High Energy Physics*,

*2011*(3), [53]. https://doi.org/10.1007/JHEP03(2011)053