Abstract
Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are probed for consistency. An isolated allowed region in parameter space is found under certain assumptions involving pushing operator dimensions above marginality, indicating the existence of a conformal field theory in this region. The obtained results have possible applications for ferromagnetic phase transitions as well as structural phase transitions in crystals. They are in tension with previous \epsilonϵ expansion results, as noticed already in earlier work.
Highlights
We present the results of our numerical exploration of φ-X mixed correlators in unitary theories with cubic symmetry
In this work we have carried out a detailed numerical analysis of theories with cubic symmetry in three dimensions
We analyzed a system of mixed four-point functions, and after experimenting with assumptions on the spectrum we managed to find an isolated region allowed by unitarity and crossing symmetry
Summary
Well as other systems, the cubic deformation is allowed in the context of the Landau theory of phase transitions, and its effects need to be taken into account in order to find the fixed point to which the flow is driven at low energies. In the past, this has been addressed mainly with perturbative methods like the expansion [1], while Monte Carlo simulations have been very limited [2]. In this work we study theories with cubic symmetry using the numerical conformal bootstrap [3]. Its OPE with itself takes the schematic form φi × φ j ∼ δi j S + X(i j) + Y(i j) + A[i j] ,
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