Decoding a Three-Dimensional Conformal Manifold

TL;DR

This paper explores the structure of a three-dimensional conformal manifold in an $ ext{N}=2$ supersymmetric theory, using both perturbative and numerical methods to analyze operator spectra and dualities.

Contribution

It provides a detailed study of the conformal manifold, including its duality group and spectrum, combining $4- ext{epsilon}$ expansion with conformal bootstrap techniques.

Findings

Good agreement between $4- ext{epsilon}$ expansion and bootstrap results

Identification of special points: XYZ model and decoupled Wess-Zumino models

Characterization of the conformal manifold as an orbifold of $ ext{CP}^1$

Abstract

We study the one-dimensional complex conformal manifold that controls the infrared dynamics of a three-dimensional $\mathcal{N}=2$ supersymmetric theory of three chiral superfields with a cubic superpotential. Two special points on this conformal manifold are the well-known XYZ model and three decoupled copies of the critical Wess-Zumino model. The conformal manifold enjoys a discrete duality group isomorphic to $S_4$ and can be thought of as an orbifold of $\mathbf{CP}^1$. We use the $4-\varepsilon$ expansion and the numerical conformal bootstrap to calculate the spectrum of conformal dimensions of low-lying operators and their OPE coefficients, and find a very good quantitative agreement between the two approaches.