Solving the 3D Ising Model with the Conformal Bootstrap

Abstract

We study the constraints of crossing symmetry and unitarity in general 3D Conformal Field Theories. In doing so we derive new results for conformal blocks appearing in four-point functions of scalars and present an efficient method for their computation in arbitrary space-time dimension. Comparing the resulting bounds on operator dimensions and OPE coefficients in 3D to known results, we find that the 3D Ising model lies at a corner point on the boundary of the allowed parameter space. We also derive general upper bounds on the dimensions of higher spin operators, relevant in the context of theories with weakly broken higher spin symmetries.

32 pages, 11 figures; v2: refs added, small changes in Section 5.3, Fig. 7 replaced; v3: ref added, fits redone in Section 5.4

References in corpus (12)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Holography from Conformal Field Theory
• Spinning Conformal Blocks
• Bounds on 4D Conformal and Superconformal Field Theories
• Carving Out the Space of 4D CFTs
• Comments on Unparticles
• Bounds in 4D Conformal Field Theories with Global Symmetry
• Central Charge Bounds in 4D Conformal Field Theory
• Conformal Bootstrap in Three Dimensions?
• Scale without Conformal Invariance at Three Loops
• Critical behavior of the Ising model with long range interactions
• Comments on scale invariant but non-conformal supersymmetric field theories

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