Correlation Functions of Coulomb Branch Operators

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.

47 pages, 6 figures. v2: typos corrected and references added

References in corpus (12)

• Notes on SUSY Gauge Theories on Three-Sphere
• Sphere Partition Functions and the Zamolodchikov Metric
• Small Instantons, Little Strings and Free Fermions
• A non-renormalization theorem for chiral primary 3-point functions
• $t{t}^{\ast }$ equations, localization and exact chiral rings in 4d N=2 SCFTs
• Gauge Theory, Ramification, And The Geometric Langlands Program
• Exact correlation functions in SU(2) N=2 superconformal QCD
• AGT on the S-duality Wall
• Constraints on Chiral Operators in N=2 SCFTs
• Supersymmetric counterterms from new minimal supergravity
• Wilson Loops and Chiral Correlators on Squashed Spheres
• Remarks on Resonant Scalars in the AdS/CFT Correspondence

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