Bootstrapping the $(A_1,A_2)$ Argyres-Douglas theory

TL;DR

This paper uses bootstrap methods to analyze the $(A_1,A_2)$ Argyres-Douglas theory, providing bounds on its spectrum and operator data, and demonstrating consistency between numerical and analytical estimates.

Contribution

It applies bootstrap techniques to a specific Argyres-Douglas theory, deriving bounds on operator dimensions and OPE coefficients, and compares numerical and inversion formula estimates.

Findings

Bounded the dimensions of semi-short multiplets up to spin 20.

Provided numerical ranges for OPE coefficients of chiral ring operators.

Estimated the dimension of the first non-protected multiplet for small spin.

Abstract

We apply bootstrap techniques in order to constrain the CFT data of the $(A_1,A_2)$ 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 $\ell$. 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 $\ell=20$. Through a recently obtained inversion formula, we also estimate them for sufficiently large $\ell$, 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.