Bootstrapping mixed correlators in the 3D Ising model

By Filip Kos, David Poland, David Simmons-Duffin. 2014

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A bstractWe 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 (Δσ, Δϵ) assuming that σ and ϵ are the only relevant scalars in the theory. These constraints yield a small closed region in (Δσ, Δϵ) space compatible with the known values in the 3D Ising CFT.

Subfields: Artificial Intelligence, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/3a394da75020a8b53193079a591cedd2603563a8

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Citations in the corpus

A proof of the conformal collider bounds (2016, neutral): “[2–5, 61–72]).”
Bootstrapping 3D fermions (2015, methodology): “This will allow us to impose gaps in the fermionic spectrum, opening up the possibility to obtain isolated islands in the space of operator dimensions, as was seen for scalar correlators in [7, 10].”
The N=2$$ \mathcal{N}=2 $$ superconformal bootstrap (2014, background): “The pioneering work of this type was [14], where three-dimensional non-supersymmetric CFTs were studied.”
Conformal invariance in the long-range Ising model (2015, methodology): “In 3d, the most dramatic evidence for the conformal invariance of the SRI critical point comes from its recent exploration using the conformal bootstrap methods [14–19, 13, 20– 22].”
TASI Lectures on the Conformal Bootstrap (2016, methodology): “the ˙ ˙OPE, where ˙is a real scalar primary in a unitary 3d CFT with a Z 2 symmetry, from [56]. This bound is computed with = 24 (78-dimensional space of derivatives). the 3d Ising CFT was studied in [60]. To get interesting new bounds in this case, it’s necessary to input an additional fact: that ˙”
The conformal bootstrap: Theory, numerical techniques, and applications (2018, positive): “This can be accomplished using a trick introduced in Kos et al. (2014b), where one discards some number of poles but compensates by modifying the residues of the kept poles.”
Analyticity in spin in conformal theories (2017, background): “eq. (3.7). These poles are all below the unitarity bound = J+d 2, but are nonetheless to the right of the contour = d=2, and so they should be included. Poles of conformal blocks were studied e.g. in [31,32]. Their possible location is heavily constrained by the Casimir equations, which imply that t”
Recursion relations for conformal blocks (2015, methodology): “This result is consistent with the result of [1, 18] (4).”
Carving out OPE space and precise O(2) model critical exponents (2019, methodology): “The setup is same as the dark blue region of figure 3 in [5] except nmax = 10 (Λ = 19).”
Boundary and interface CFTs from the conformal bootstrap (2015, methodology): “This strategy was applied to the 3d Ising model in [24], providing strong evidence that the presence of Z2 symmetry and two relevant primaries defines only one theory.”
Bootstrapping the O(N) archipelago (2015, neutral): “Note that we are following the conformal block conventions of [51], which contain a factor of (−1) relative to the conventions used in the previous global symmetry studies [10, 15].”
Bootstrapping SCFTs with four supercharges (2015, neutral): “J H E P 0 8 ( 2 0 1 5 ) 1 4 2 accuracy [9–12].”
Exact correlators of BPS Operators from the 3d superconformal bootstrap (2014, background): “In most examples, crossing symmetry is combined with unitarity and is implemented numerically on various four-point functions (see, for example, [12–43]).”
EPFL Lectures on Conformal Field Theory in D ≥ 3 Dimensions (2016, methodology): “This happens for the 3d Ising model [46, 47] and for the O(N) models [48].”
Weight shifting operators and conformal blocks (2017, neutral): “In numerical conformal bootstrap one usually requires simple rational approximations to conformal blocks [8, 22, 30], which are hard to construct from these expressions.”
The nonperturbative functional renormalization group and its applications (2020, result): “Vertical lines indicate the value αopt obtained from the PMS and the horizontal dashed lines the conformal bootstrap results [1342].”
The lightcone bootstrap and the spectrum of the 3d Ising CFT (2016, methodology): “A.3 Several operators in the 3d Ising CFT In this section, we list dimensions and OPE coefficients of 112 stable operators obtained from the calculation described in section A.1 (and plotted in figures 1 and 2).”
A scaling theory for the long-range to short-range crossover and an infrared duality (2017, methodology): “42) (19)Beware of the changes in normalization of OPE coefficients between [21] and [35, 16], explained in appendix A.”