Correlation functions of Coulomb branch operators
Abstract
We consider the correlation functions of Coulomb branch operators in fourdimensional N = 2 Superconformal Field Theories (SCFTs) involving exactly one antichiral operator. These extremal correlators are the "minimal" nonholomorphic local observables in the theory. We show that they can be expressed in terms of certain determinants of derivatives of the foursphere partition function of an appropriate deformation of the SCFT. This relation between the extremal correlators and the deformed foursphere partition function is nontrivial due to the presence of conformal anomalies, which lead to operator mixing on the sphere. Evaluating the deformed foursphere 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 fourdimensional 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.
 Publication:

Journal of High Energy Physics
 Pub Date:
 January 2017
 DOI:
 10.1007/JHEP01(2017)103
 arXiv:
 arXiv:1602.05971
 Bibcode:
 2017JHEP...01..103G
 Keywords:

 Conformal Field Theory;
 Supersymmetric gauge theory;
 Anomalies in Field and String Theories;
 Supersymmetry and Duality;
 High Energy Physics  Theory
 EPrint:
 47 pages, 6 figures. v2: typos corrected and references added