Bootstrapping (D, D) Conformal Matter

TL;DR

This paper employs the numerical conformal bootstrap to analyze six-dimensional superconformal field theories, providing evidence for bounds saturation, verifying chiral-ring relations, and exploring operator product expansion rules.

Contribution

It demonstrates that minimal (D_k, D_k) conformal matter saturates unitarity bounds and uses extremal-functional methods to verify relations and uncover new OPE selection rules.

Findings

Minimal (D_k, D_k) conformal matter saturates unitarity bounds.

Chiral-ring relations are correctly reproduced.

Hints of novel OPE selection rules involving type-B multiplets.

Abstract

We use the numerical conformal bootstrap to study six-dimensional $\mathcal{N}=(1,0)$ superconformal field theories with flavor symmetry $\mathfrak{so}_{4k}$. We present evidence that minimal $(D_k, D_k)$ conformal matter saturates the unitarity bounds for arbitrary $k$. Furthermore, using the extremal-functional method, we check that the chiral-ring relations are correctly reproduced, extract the anomalous dimensions of low-lying long superconformal multiplets, and find hints for novel OPE selection rules involving type-$\mathcal{B}$ multiplets.