  We propose a non-perturbative definition for refined topological strings.
This can be used to compute the partition function of superconformal theories
in 5 dimensions on squashed S^5 and the superconformal index of a large number
of 6 dimensional (2,0) and (1,0) theories, including that of N coincident M5
branes. The result can be expressed as an integral over the product of three
combinations of topological string amplitudes. SL(3,Z) modular transformations
acting by inverting the coupling constants of the refined topological string
play a key role.
