Journal of High Energy Physics· 2014Q2
Bootstrapping mixed correlators in the 3D Ising model
- 292citations
- Q2SCImago
- 2014year
Short summary
We numerically constrain operator dimensions in 3D CFTs with Z2 symmetry by applying the conformal bootstrap to mixed correlators, yielding a small region compatible with the 3D Ising model.
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Key points
- The conformal bootstrap is applied to mixed correlators of non-identical operators in 3D CFTs with Z2 symmetry.
- Crossing symmetry and unitarity constraints are formulated using semidefinite programming.
- Numerical constraints are derived for the dimensions of the leading Z2-odd (sigma) and Z2-even (epsilon) scalar operators.
- A small, closed region in (Delta_sigma, Delta_epsilon) space is obtained, consistent with the 3D Ising CFT.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study the conformal bootstrap for systems of correlators involving nonidentical operators. The constraints of crossing symmetry and unitarity for such mixed correlators can be phrased in the language of semidefinite programming. We apply this formalism to the simplest system of mixed correlators in 3D CFTs with a ℤ2 global symmetry. For the leading ℤ2-odd operator σ and ℤ2-even operator ϵ, we obtain numerical constraints on the allowed dimensions (Δ σ , Δ ϵ ) assuming that σ and ϵ are the only relevant scalars in the theory. These constraints yield a small closed region in (Δ σ , Δ ϵ ) space compatible with the known values in the 3D Ising CFT.
The authors' abstract, as published at the source. Journal of High Energy Physics, 2014 · DOI ↗
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Field: Numerical Analysis
Numerical AnalysisMathematics