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.
Deformation quantization of Poiss on manifolds
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Proves UV finiteness and dimension-dependent vanishing of anomaly obstructions for topological-holomorphic field theories on R^{d'} × C^d, allowing consistent quantization via factorization algebras.
Fluid dynamics is formulated as an intersection problem on a symplectic manifold associated with spacetime, yielding a geometric derivation of covariant hydrodynamics and extensions to multicomponent and anomalous fluids.
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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.
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On the renormalization and quantization of topological-holomorphic field theories
Proves UV finiteness and dimension-dependent vanishing of anomaly obstructions for topological-holomorphic field theories on R^{d'} × C^d, allowing consistent quantization via factorization algebras.
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Fluid dynamics as intersection problem
Fluid dynamics is formulated as an intersection problem on a symplectic manifold associated with spacetime, yielding a geometric derivation of covariant hydrodynamics and extensions to multicomponent and anomalous fluids.