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.
Highlights
For the last three decades, string theory has been a potent apparatus for the construction of quantum field theories (QFTs)
Conformal field theories (CFTs) are an especially interesting class of QFTs; they exist at the fixed points of the renormalization group flows, and they can provide important insights into the nature of quantum field theory
Our focus is on CFTs with additional supersymmetry, known as superconformal field theories (SCFTs)
Summary
For the last three decades, string theory has been a potent apparatus for the construction of quantum field theories (QFTs). There is a seemingly consistent spectrum with su flavor symmetry, for which the Higgs branch is the oneinstanton moduli space of SUð3Þ [12]; this theory does not have a known geometric construction It is an open question, which can be considered as part of the swampland program, whether all consistent 6D SCFTs have an origin in string theory. The bounds that are imposed by crossing symmetry and associativity of the OPE appear to be saturated by SCFTs that have a construction via string theory. Another interesting feature of a 6D SCFT, and one which can be gainfully employed in a superconformal bootstrap approach, is the associated Higgs branch This is the hyperKähler moduli space where the half-BPS states gain vacuum expectation values and as such it is a more refined property than the numerical value of CJ. Provide an additional cross-check to the claim that conformal matter saturates unitarity bounds
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