Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology· 2012
Solving the 3D Ising model with the conformal bootstrap
- 712citations
- 2012year
Short summary
The 3D Ising model is found to lie at a unique 'corner point' of allowed parameter space, determined by the conformal bootstrap method which constrains theories using crossing symmetry and unitarity.
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Key points
- New results for conformal blocks in four-point scalar functions were derived.
- An efficient method for computing conformal blocks in arbitrary dimensions was presented.
- The 3D Ising model was identified at a unique 'corner point' of the allowed parameter space.
- General upper bounds on higher spin operator dimensions were derived.
AI-generated from the title and abstract; the full text is not read.
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 product-expansion 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.
The authors' abstract, as published at the source. Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D, Particles, fields, gravitation, and cosmology, 2012 · DOI ↗
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Field: Condensed Matter Physics
Condensed Matter PhysicsPhysics and Astronomy