The string geometry behind topological amplitudes

It is shown that the generating function of N = 2 topological strings, in the heterotic weak coupling limit, is identified with the partition function of a six-dimensional Melvin background. This background, which corresponds to an exact CFT, realises in string theory the six-dimensional Ω-background of Nekrasov, in the case of opposite deformation parameters ϵl = −ϵ2, thus providing the known perturbative part of the Nekrasov partition function in the field theory limit. The analysis is performed on both heterotic and type I strings and for the cases of ordinary N = 2 and N = 2* theories.