The lightcone bootstrap and the spectrum of the 3d Ising CFT

By David Simmons-Duffin. 2016

296 citations recorded by the source corpus.

We compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is a set of new techniques for computing infinite sums of SL(2, ℝ$$ \mathrm{\mathbb{R}} $$) conformal blocks. Using these techniques, we solve the lightcone bootstrap to all orders in an asymptotic expansion in large spin, and suggest a strategy for going beyond the large spin limit. We carry out the first steps of this strategy for the 3d Ising CFT, deriving analytic approximations for the dimensions and OPE coefficients of several infinite families of operators in terms of the initial data {Δσ, Δϵ, fσσϵ, fϵϵϵ, cT}. The analytic results agree with numerics to high precision for about 100 low-twist operators (correctly accounting for O(1) mixing effects between large-spin families). Plugging these results back into the crossing equations, we obtain approximate analytic constraints on the initial data.

Subfields: Geometry and Topology, Nuclear and High Energy Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/47942d8bdbf1c9f590c6f5a143d69f1f0b4baf08

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Citations in the corpus

The conformal bootstrap: Theory, numerical techniques, and applications (2018, methodology): “51 We followed the presentation in (Simmons-Duffin, 2017b, section 9.3).”
Light-ray operators in conformal field theory (2018, methodology): “Caron-Huot’s Lorentzian inversion formula has many other useful applications, for example to large-spin perturbation theory and the lightcone bootstrap [17–26], and to the SYK model [27–30].”
A scaling theory for the long-range to short-range crossover and an infrared duality (2017, background): “42) (19)Beware of the changes in normalization of OPE coefficients between [21] and [35, 16], explained in appendix A.”
Analyticity in spin in conformal theories (2017, methodology): “This assumption has been confirmed in explicit examples, for instance in the three-dimensional Ising model again, where the resulting expansion appears to remain accurate all the way down to spin two [10, 11]! Gaining control over the errors in this expansion will be crucial to mesh it with numerica”
The nonperturbative functional renormalization group and its applications (2020, methodology): “Table 1: Critical exponents ν, η andω for the three-dimensional O(N) universality class obtained in the FRG approach from DE to second [115, 116], fourth [117] and sixth [118] orders, LPA′′ [119, 120] and BMW approximation [121, 122], compared to Monte Carlo (MC) simulations [123–128], d = 3 perturb”
Carving out OPE space and precise O(2) model critical exponents (2019, methodology): “For example, in [97, 98], it was shown using the lightcone bootstrap that crossing symmetry for the operators σ, in the 3d Ising model can be approximately recast as a set of constraints for a small amount of low-twist data, namely ∆σ,∆ , λσσ , λ , and cT .”