Deformations in algebraic superstring models indicate a non-algebraic generalization that aligns with mirror duality requirements.
Haploid (2,2)-superfields in 2-dimensional space-time
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abstract
Superfields in 2-dimensional (2,2)-superspacetime which are independent of (some) half of the fermionic coordinates are discussed in a hopefully both comprehensive and comprehensible manner. An embarrassing abundance of these simplest `building blocks' makes it utterly impossible to write down the `most general Lagrangian'. With some ad hoc but perhaps plausible restrictions, a rather general Lagrangian is found, which exhibits many of the phenomena that have been studied recently, and harbors many more. In particular, it becomes patently obvious that the (2,2)-supersymmetric 2-dimensional field theory target space geometries (many of which are suitable for (super)string propagation) are far more general than Kahler manifolds with holomorphic bundles.
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Generalizations beyond algebraic geometry in string theory remain aligned with mirror symmetry, support quantitative analysis, and point to deeper symplectic geometry connections.
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Beyond Algebraic Superstring Compactification: Part II
Deformations in algebraic superstring models indicate a non-algebraic generalization that aligns with mirror duality requirements.
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Beyond Algebraic Solutions to Stringy Spacetime
Generalizations beyond algebraic geometry in string theory remain aligned with mirror symmetry, support quantitative analysis, and point to deeper symplectic geometry connections.