Correlation Functions of Coulomb Branch Operators

TL;DR

This paper derives exact formulas for extremal correlation functions of Coulomb branch operators in 4D N=2 SCFTs, linking them to deformed four-sphere partition functions and revealing their integrable structure.

Contribution

It establishes a novel relation between extremal correlators and deformed four-sphere partition functions using localization, and uncovers their integrable differential equations.

Findings

Explicit computation of extremal correlators in various SCFT examples.

Derivation of integrable differential equations governing correlators.

Comparison with perturbative results and tt* equations.

Abstract

We consider the correlation functions of Coulomb branch operators in four-dimensional N=2 Superconformal Field Theories (SCFTs) involving exactly one anti-chiral 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.