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 S4 and can be thought of as an orbifold of CP1. We use the 4 − ε 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.
Highlights
Conformal manifolds are the manifolds parametrized by the exactly marginal coupling constants of a given conformal field theory (CFT)
As shown in [7] using an abstract approach, the superconformal algebra allows for the existence of marginal couplings only in superconformal field theories (SCFTs) with N = 1 or 2 supersymmetry in 3d and N = 1, 2, or 4 supersymmetry in 4d
We argue that for generic hi, the theory flows to a family of strongly interacting CFTs with N = 2 superconformal symmetry, parametrized by the ratio of the coupling constants6 τ = h2 . h1 (2.5)
Summary
Conformal manifolds are the manifolds parametrized by the exactly marginal coupling constants of a given conformal field theory (CFT). To the best of our knowledge this is the first time the numerical conformal bootstrap program has been applied successfully as a function of a marginal coupling in d > 2.3 The results from the conformal bootstrap are non-perturbative in nature and are applicable directly to the strongly coupled theory in three dimensions. They confirm the general qualitative analysis based on symmetries and dualities and match the perturbative 4 − ε expansion to remarkable precision. We summarize some results about the 2d analogue of the model (1.2) in appendix D
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