### Abstract

We consider the correlation functions of Coulomb branch operators in four-dimensional N = 2 Superconformal Field Theories (SCFTs) involving exactly one antichiral operator. These extremal correlators are the “minimal” non-holomorphic local observables in the theory. We show that they can be expressed in terms of certain determinants of derivatives of the four-sphere partition function of an appropriate deformation of the SCFT. This relation between the extremal correlators and the deformed four-sphere partition function is non-trivial due to the presence of conformal anomalies, which lead to operator mixing on the sphere. Evaluating the deformed four-sphere partition function using supersymmetric localization, we compute the extremal correlators explicitly in many interesting examples. Additionally, the representation of the extremal correlators mentioned above leads to a system of integrable differential equations. We compare our exact results with previous perturbative computations and with the four-dimensional tt^{∗} equations. We also use our results to study some of the asymptotic properties of the perturbative series expansions we obtain in N = 2 SQCD.

Original language | English (US) |
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Article number | 103 |

Journal | Journal of High Energy Physics |

Volume | 2017 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2017 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- Anomalies in Field and String Theories
- Conformal Field Theory
- Supersymmetric gauge theory
- Supersymmetry and Duality

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## Cite this

*Journal of High Energy Physics*,

*2017*(1), [103]. https://doi.org/10.1007/JHEP01(2017)103