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The conformal bootstrap

Nature Physics volume 12, pages 535–539 (2016)Cite this article

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Abstract

The conformal bootstrap was proposed in the 1970s as a strategy for calculating the properties of second-order phase transitions. After spectacular success elucidating two-dimensional systems, little progress was made on systems in higher dimensions until a recent renaissance beginning in 2008. We report on some of the main results and ideas from this renaissance, focusing on new determinations of critical exponents and correlation functions in the three-dimensional Ising and O(N) models.

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Figure 1: Sum rule geometry.
Figure 2: Ising Δε upper bound.
Figure 3: Ising critical exponents.
Figure 4: O(N) singlet upper bounds.
Figure 5: O(N) archipelago.

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  1. Department of Physics, Yale University, New Haven, Connecticut 06520, USA

    David Poland

  2. School of Natural Sciences, Institute for Advanced Study, Princeton, New Jersey 08540, USA

    David Poland & David Simmons-Duffin

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Correspondence to David Simmons-Duffin.

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Poland, D., Simmons-Duffin, D. The conformal bootstrap. Nature Phys 12, 535–539 (2016). https://doi.org/10.1038/nphys3761

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