Worldsheet realization of the refined topological string

A worldsheet realization of the refined topological string is proposed in terms of physical string amplitudes that compute generalized image F-terms of the form image in the effective supergravity action. These terms involve the chiral Weyl superfield W and a superfield ϒ defined as an image chiral projection of a particular anti-chiral image-vector multiplet. In Heterotic and Type I theories, obtained upon compactification on the six-dimensional manifold image, T is the usual Kähler modulus of the image torus. These amplitudes are computed exactly at the one-loop level in string theory. They are shown to reproduce the correct perturbative part of the Nekrasov partition function in the field theory limit when expanded around an image enhancement point of the string moduli space. The two deformation parameters image and image of the Ω supergravity background are then identified with the constant field strength backgrounds for the anti-self-dual graviphoton and self-dual gauge field of the image vector multiplet, respectively.