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Non-critical strings, del Pezzo singularities and Seiberg-Witten curves. (English) Zbl 0934.81036
Summary: We study limits of four-dimensional type II Calabi-Yau compactifications with vanishing 4-cycle singularities, which are dual to \(T^2\) compactifications of the six-dimensional non-critical string with \(E_8\) symmetry. We define proper sub-sectors 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.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
14B05 Singularities in algebraic geometry
32J81 Applications of compact analytic spaces to the sciences
81T60 Supersymmetric field theories in quantum mechanics
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