6D large charge and 2D Virasoro blocks

We compute observables in the interacting rank-one 6D <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi mathvariant="script">N</a:mi><a:mo>=</a:mo><a:mo stretchy="false">(</a:mo><a:mn>2</a:mn><a:mo>,</a:mo><a:mn>0</a:mn><a:mo stretchy="false">)</a:mo></a:math> superconformal field theory (SCFT) at large <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"><f:mi>R</f:mi></f:math>-charge. We focus on correlators involving <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:msup><h:mi mathvariant="normal">Φ</h:mi><h:mi>n</h:mi></h:msup></h:math>, namely symmetric products of the bottom component of the supermultiplet containing the stress tensor. By using the moduli space effective action and methods from the large-charge expansion, we compute the operator product expansion coefficients <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mo stretchy="false">⟨</k:mo><k:mrow><k:msup><k:mi mathvariant="normal">Φ</k:mi><k:mi>n</k:mi></k:msup><k:msup><k:mi mathvariant="normal">Φ</k:mi><k:mi>m</k:mi></k:msup><k:msup><k:mi mathvariant="normal">Φ</k:mi><k:mrow><k:mi>n</k:mi><k:mo>+</k:mo><k:mi>m</k:mi></k:mrow></k:msup></k:mrow><k:mo stretchy="false">⟩</k:mo></k:math> in an expansion in <r:math xmlns:r="http://www.w3.org/1998/Math/MathML" display="inline"><r:mn>1</r:mn><r:mo>/</r:mo><r:mi>n</r:mi></r:math>. The coefficients of the expansion are only partially determined from the 6D perspective, but we manage to fix them order-by-order in <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:mn>1</t:mn><t:mo>/</t:mo><t:mi>n</t:mi></t:math> numerically by utilizing the <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline"><v:mrow><v:mn>6</v:mn><v:mi mathvariant="normal">D</v:mi><v:mo>/</v:mo><v:mn>2</v:mn><v:mi mathvariant="normal">D</v:mi></v:mrow></v:math> correspondence. This is made possible by the fact that this 6D observable can be extracted in 2D from a specific double-scaling limit of the vacuum Virasoro block, which can be efficiently computed numerically. We also extend the computation to higher-rank SCFTs, and discuss various applications of our results to 6D as well as 2D.