On four dimensional N=3 superconformal theories

TL;DR

This paper investigates the theoretical properties of hypothetical four-dimensional N=3 superconformal theories, exploring their anomalies, deformations, and operator dimensions, despite no known examples existing.

Contribution

It provides a detailed analysis of the constraints and properties such theories must satisfy, including anomaly relations and the absence of certain deformations, advancing understanding of N=3 superconformal symmetry.

Findings

Conformal anomalies obey a=c.

No exactly marginal N=3 preserving deformations exist.

Possible dimensions of chiral operators are constrained.

Abstract

In this note we study four dimensional theories with N=3 superconformal symmetry, that do not also have N=4 supersymmetry. No examples of such theories are known, but their existence is also not ruled out. We analyze several properties that such theories must have. We show that their conformal anomalies obey a=c. Using the N=3 superconformal algebra, we show that they do not have any exactly marginal deformations preserving N=3 supersymmetry, or global symmetries (except for their R-symmetries). Finally, we analyze the possible dimensions of chiral operators labeling their moduli space.