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arXiv · 1109.5728

The Omega deformed B-model for rigid N=2 theories

Min-xin Huang·Amir-Kian Kashani-Poor·Albrecht Klemm
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Abstract

We give an interpretation of the Omega deformed B-model that leads naturally to the generalized holomorphic anomaly equations. Direct integration of the latter calculates topological amplitudes of four dimensional rigid N=2 theories explicitly in general Omega-backgrounds in terms of modular forms. These amplitudes encode the refined BPS spectrum as well as new gravitational couplings in the effective action of N=2 supersymmetric theories. The rigid N=2 field theories we focus on are the conformal rank one N=2 Seiberg-Witten theories. The failure of holomorphicity is milder in the conformal cases, but fixing the holomorphic ambiguity is only possible upon mass deformation. Our formalism applies irrespectively of whether a Lagrangian formulation exists. In the class of rigid N=2 theories arising from compactifications on local Calabi-Yau manifolds, we consider the theory of local P2. We calculate motivic Donaldson-Thomas invariants for this geometry and make predictions for generalized Gromov-Witten invariants at the orbifold point.

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Min-xin Huang, Amir-Kian Kashani-Poor, Albrecht Klemm. 2013-02-07. The Omega deformed B-model for rigid N=2 theories. https://doi.org/10.1007/s00023-012-0192-x

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