Bootstrapping Mixed Correlators in Three-Dimensional Cubic Theories

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 $\epsilon$ expansion results, as noticed already in earlier work.

arXiv comment14 pages, 7 figures. v2: minor emendations. v3: References added, typos fixed, some additions/clarifications. v4: Another reference added, more typos fixed, some more additions/clarifications; v5: Fixed typos in eqs. (2.16), (2.20), (2.23)

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• Exploring $SU(N)$ adjoint correlators in $3d$
• Superconformal Blocks for Mixed 1/2-BPS Correlators with $SU(2)$ R-symmetry
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• Bootstrapping Mixed MN Correlators in 3D
• Navigating through the O(N) archipelago
• Analytic and numerical bootstrap for the long-range Ising model
• The tricritical Ising CFT and conformal bootstrap
• Critical behavior of weakly disordered Ising model: Six-loop $\sqrt{\epsilon }$ expansion study
• Anomalous Dimensions in Hypercubic Theories
• Crossover exponents, fractal dimensions and logarithms in Landau-Potts field theories
• Possibility of a continuous phase transition in random-anisotropy magnets with ageneric random-axis distribution
• Conformal Bootstrap with Duality-Inspired Fusion Rule
• The Cubic Fixed Point at Large $N$