On Non-renormalization and OPE in Superconformal Field Theories

Abstract

The OPE of two N=2 R-symmetry current (short) multiplets is determined by the possible superspace three-point functions that two such multiplets can form with a third, a priori long multiplet. We show that the shortness conditions on the former put strong restrictions on the quantum numbers of the latter. In particular, no anomalous dimension is allowed unless the third supermultiplet is an R-symmetry singlet. This phenomenon should explain many known non-renormalization properties of correlation functions, including the one of four stress-tensor multiplets in N=4 SYM_4.

minor corrections, references changed

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• Properties of the Konishi multiplet in N=4 SYM theory
• Protected Operators in N=2,4 Supersymmetric Theories
• Nonrenormalization theorems for N=2 Super Yang-Mills

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