Non-Perturbative Topological String Partition Function on Twisted Affine Line Bundle over C×T2

Using the instanton partition function for five-dimensional U(1) gauge theory with eight supercharges and a single adjoint massive hypermultiplet on the Ω background, we give explicit expression for non-perturbative corrections to the topological string theory in the holomorphic limit. It was argued that in this case the theory is compactified on the twisted affine line bundle over C×T2. We perform calculations in two ways. First we modify the integration contour by adding poles responsible for non-perturbative physics in accordance with a recent proposal. Then, we compute the genus zero Gopakumar–Vafa invariants for our case and evaluate the non-perturbative corrections to the partition function. We check that both calculations give the same result.