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Mirror Manifolds And Topological Field Theory
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abstract
These notes are devoted to explaining aspects of the mirror manifold problem that can be naturally understood from the point of view of topological field theory. Basically this involves studying the topological field theories made by twisting $N=2$ sigma models. This is mainly a review of old results, except for the discussion in \S7 of certain facts that may be relevant to constructing the ``mirror map'' between mirror moduli spaces.
Forward citations
Cited by 11 Pith papers
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Monodromy defects in Chern-Simons theory and Holography
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Worldsheet Duals to One-Matrix Models
A B-twisted Landau-Ginzburg model plus topological gravity on the worldsheet is shown to be the exact dual of any interacting one-matrix model, with matrix traces mapping directly to vertex operators and correlators a...
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Toward the Structure Constants of $\mathcal{N}=2$ Liouville Theory
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Line Operators in 3d Holomorphic QFT: Meromorphic Tensor Categories and dg-Shifted Yangians
In 3d holomorphic-topological QFTs, line operators and their OPEs are controlled by a Koszul-dual A-infinity algebra carrying a dg-shifted Yangian structure with a degree-1 r-matrix.
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Black Hole Entropy, Quantum Corrections and EFT Transitions
Quantum corrections to BPS black hole entropy in 4d N=2 string compactifications can be resummed into a finite formula that interpolates between four- and five-dimensional EFT descriptions and matches exact 5d microst...
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A-type Sigma Models from Differential Poisson Geometry
Symplectic reduction of the differential Poisson sigma model yields a restricted class of classical A-type models whose quartic curvature coupling is induced by torsion of a flat connection, with the Kodaira–Thurston ...
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BPS Invariants for Generalized Toric Calabi-Yau Threefolds
Gopakumar–Vafa invariants are transported across Hanany–Witten transitions after removing a universal parallel-brane sector, giving first-time high-degree invariants for local dP4.
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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.
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Nil-Equivariant Tropological Sigma Models on Filtered Geometries
Tropological sigma models on 4D targets are defined on filtered manifolds with nilpotent Engel algebra symmetries and conjectured to correspond to filtered Gromov-Witten invariants.
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Tropical Branes
Quantizing open tropical strings with Dirichlet or Neumann boundary conditions gives a Hamiltonian of free, non-oscillating modes, named tropical branes, proposed to describe asymptotic on-shell string states.
- Lecture notes on conformal field theory
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