Emergent Geometry and Mirror Symmetry of A Point
Jian Zhou
TL;DR
This paper explores the connection between topological 2D gravity and mirror symmetry, revealing a conformal field theory on the Airy curve as the mirror of Gromov-Witten theory of a point, and deriving related formulas.
Contribution
It introduces a novel mirror theory for Gromov-Witten theory of a point using topological 2D gravity and formulates bosonic n-point functions in terms of fermionic 2-point functions.
Findings
Identification of a conformal field theory on the Airy curve as the mirror
Derivation of a formula relating bosonic n-point functions to fermionic 2-point functions
Establishment of a link between topological 2D gravity and mirror symmetry
Abstract
By considering the partition function of the topological 2D gravity, a conformal field theory on the Airy curve emerges as the mirror theory of Gromov-Witten theory of a point. In particular, a formula for bosonic n-point functions in terms of fermionic 2-point function for this theory is derived.
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Taxonomy
TopicsNonlinear Waves and Solitons · Mathematics and Applications · Algebraic and Geometric Analysis