The String Geometry Behind Topological Amplitudes

Abstract

It is shown that the generating function of $\mathcal{N}=2$ 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 $\Omega$-background of Nekrasov, in the case of opposite deformation parameters ${\epsilon }_1=-{\epsilon }_2$, 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 $\mathcal{N}=2$ and $\mathcal{N}=2^{\ast }$ theories.

28 pages

References in corpus (3)

• Instanton calculus in R-R background and the topological string
• Exotic instanton counting and heterotic/type I' duality
• Alpha- and Omega-Deformations from fluxes in M-Theory

Cited by in corpus (1)

• Refined Topological Amplitudes from the $\Omega$-Background in String Theory