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We study limits of four-dimensional type II Calabi-Yau compactifications with vanishing four-cycle singularities, which are dual to $IT^2$ compactifications of the six-dimensional non-critical string with $E_8$ symmetry. We define proper subsectors of the full string theory, which can be consistently decoupled. In this way we obtain rigid effective theories that have an intrinsically stringy BPS spectrum. Geometrically the moduli spaces correspond to special geometry of certain non-compact Calabi-Yau spaces of an intriguing form. An equivalent description can be given in terms of Seiberg-Witten curves, given by the elliptic simple singularities together with a peculiar choice of meromorphic differentials. We speculate that the moduli spaces describe non-perturbative non-critical string theories.
We consider N=2 supersymmetric gauge theories perturbed by tree level superpotential terms near isolated singular points in the Coulomb moduli space. We identify the Seiberg-Witten curve at these points with polynomial equations used to construct wha
We show how to map Grothendiecks dessins denfants to algebraic curves as Seiberg-Witten curves, then use the mirror map and the AGT map to obtain the corresponding 4d $mathcal{N}=2$ supersymmetric instanton partition functions and 2d Virasoro conform
We derive Seiberg-Witten like equations encoding the dynamics of N=2 ADE quiver gauge theories in presence of a non-trivial Omega-background along a two dimensional plane. The epsilon-deformed prepotential and the chiral correlators of the gauge theo
We study the dynamics of a N=2 supersymmetric SU(N) gauge theory with fundamental or adjoint matter in presence of a non trivial Omega-background along a two dimensional plane. The prepotential and chiral correlators of the gauge theory can be obtain
We derive a family of matrix models which encode solutions to the Seiberg-Witten theory in 4 and 5 dimensions. Partition functions of these matrix models are equal to the corresponding Nekrasov partition functions, and their spectral curves are the S