Worldsheet Realization of the Refined Topological String

Abstract

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 F_{g,n} W^{2g}Y^{2n} in the effective supergravity action. These terms involve the chiral Weyl superfield W and a superfield Y defined as an N=2 chiral projection of a particular anti-chiral T-bar vector multiplet. In Heterotic and Type I theories, obtained upon compactification on the six-dimensional manifold K3xT2, 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 epsilon_- and epsilon_+ of the Omega-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-bar vector multiplet, respectively.

arXiv comment35 pages, typos corrected, published in NPB

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• Omega-Deformed Seiberg-Witten Effective Action from the M5-brane
• Exact partition functions for the $\Omega$-deformed $\mathcal{N}=2^{\ast }$ $SU(2)$ gauge theory
• Diagrammatic Expansion of Non-Perturbative Little String Free Energies
• Chiral trace relations in $\Omega$-deformed $\mathcal{N}=2$ theories
• Symmetric Orbifold Theories from Little String Residues
• Exact partition functions for deformed $\mathcal{N}=2$ theories with $N_f=4$ flavours
• Instanton Corrections for m and Omega
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• Resurgence of Refined Topological Strings and Dual Partition Functions
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