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 N=2 F-terms of the form Fg,nW2gϒ2n in the effective supergravity action. These terms involve the chiral Weyl superfield W and a superfield ϒ defined as an N=2 chiral projection of a particular anti-chiral T¯-vector multiplet. In Heterotic and Type I theories, obtained upon compactification on the six-dimensional manifold K3×T2, T is the usual Kähler modulus of the T2 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 SU(2) enhancement point of the string moduli space. The two deformation parameters ϵ− and ϵ+ 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 T¯ vector multiplet, respectively.