Symmetry enhancements via 5d instantons, \( q\mathcal{W} \)-algebrae and (1, 0) superconformal index

We explore $$ \mathcal{N}=\left(1,0\right) $$ superconformal six-dimensional theories arising from M5 branes probing a transverse A k singularity. Upon circle compactification to 5 dimensions, we describe this system with a dual pq-web of five-branes and propose the spectrum of basic five-dimensional instanton operators driving global symmetry enhancement. For a single M5 brane, we find that the exact partition function of the 5d quiver gauge theory matches the 6d (1, 0) index, which we compute by letter counting. We finally show that S-duality of the pq-web implies new relations among vertex correlators of $$ q\mathcal{W} $$ algebrae.