The conformal bootstrap

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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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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