An explicit Poisson vertex algebra A is proposed as the perturbative holomorphic-topological observables of pure SU(2) Seiberg-Witten theory; its series refines the Schur index and a differential Q_inst is introduced whose cohomology is hypothesized to capture non-perturbative corrections.
Topological Mirrors and Quantum Rings
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Aspects of duality and mirror symmetry in string theory are discussed. We emphasize, through examples, the importance of loop spaces for a deeper understanding of the geometrical origin of dualities in string theory. Moreover we show that mirror symmetry can be reformulated in very simple terms as the statement of equivalence of two classes of topological theories: Topological sigma models and topological Landau-Ginzburg models. Some suggestions are made for generalization of the notion of mirror symmetry.
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Poisson Vertex Algebra of Seiberg-Witten Theory
An explicit Poisson vertex algebra A is proposed as the perturbative holomorphic-topological observables of pure SU(2) Seiberg-Witten theory; its series refines the Schur index and a differential Q_inst is introduced whose cohomology is hypothesized to capture non-perturbative corrections.