Abstract
We apply bootstrap techniques in order to constrain the CFT data of the (A1, A2) Argyres-Douglas theory, which is arguably the simplest of the Argyres-Douglas models. We study the four-point function of its single Coulomb branch chiral ring generator and put numerical bounds on the low-lying spectrum of the theory. Of particular interest is an infinite family of semi-short multiplets labeled by the spin ℓ. Although the conformal dimensions of these multiplets are protected, their three-point functions are not. Using the numerical bootstrap we impose rigorous upper and lower bounds on their values for spins up to ℓ = 20. Through a recently obtained inversion formula, we also estimate them for sufficiently large ℓ, and the comparison of both approaches shows consistent results. We also give a rigorous numerical range for the OPE coefficient of the next operator in the chiral ring, and estimates for the dimension of the first R-symmetry neutral non-protected multiplet for small spin.
Highlights
Results of [35] imply that any 4d N 2 superconformal field theory (SCFT) contains a closed subsector isomorphic to a 2d chiral algebra
We study the four-point function of its single Coulomb branch chiral ring generator and put numerical bounds on the low-lying spectrum of the theory
To the 3d Ising model and O(N ) models, known supersymmetric theories appear on special points, “kinks”, of the numerically produced exclusion curves, and the numerical machinery of [1] can be applied in order to extract the CFT data
Summary
Our angle to attack the (A1, A2) theory is through its Coulomb branch, and we are interested in the N = 2 chiral and anti-chiral operators, respectively Er and Er multiplets, using the naming conventions of [68]. Considering all four-point functions involving the superconformal primaries of these multiplets, we write down the OPE selection rules and conformal block decompositions for all of the channels, and the crossing equations to be studied in sections 3 and 4. While the short multiplets being exchanged in this channel have their dimensions fixed by supersymmetry, their OPE coefficients are not known. The E2r multiplet corresponds to an operator in the Coulomb branch chiral ring and must be present in the (A1, A2) theory, the value of its OPE coefficient is not known. The contribution of the short multiplets E2r and C0,2r−1(j−1,j) is isolated from the continuous spectrum of long operators by a gap; this will be relevant for the numerical analysis of section 3
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