$\hat{Z}$ at large $N$: from curve counts to quantum modularity

Tobias Ekholm, Angus Gruen, Sergei Gukov +3

Reducing a 6d fivebrane theory on a 3-manifold $Y$ gives a $q$-series 3-manifold invariant $\hat{Z}(Y)$. We analyse the large-$N$ behaviour of $F_K=\hat{Z}(M_K)$, where $M_…