Correlation functions of Coulomb branch operators

Efrat Gerchkovitz, Jaume Gomis, Nafiz Ishtiaque, Avner Karasik, Zohar Komargodski, Silviu S. Pufu

Research output: Contribution to journalArticlepeer-review

102 Scopus citations


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 languageEnglish (US)
Article number103
JournalJournal of High Energy Physics
Issue number1
StatePublished - Jan 1 2017

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


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


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