Thermodynamic limit of Nekrasov partition function for 5-brane web with O5-plane

A bstract In this paper, we study 5d $$ \mathcal{N} N = 1 Sp( N ) gauge theory with f ( ≤ 2 + 3) flavors based on 5-brane web diagram O 5-plane. On the one hand, discuss Seiberg-Witten curve dual graph of other compute Nekrasov partition function topological vertex formalism Rewriting it in terms profile functions, obtain saddle point equation for after taking thermodynamic limit. By introducing resolvent, derive and its boundary conditions as well relation to prepotential cycle integrals. They coincide those directly obtained from This agreement gives further evidence mirror symmetry which relates case orientifold plane shed light non-toric Calabi-Yau 3-folds including D-type singularities.