On a complex-symplectic mirror pair
Quantum Algebra
2025-02-18 v1 High Energy Physics - Theory
Algebraic Geometry
Abstract
We study the canonical Poisson structure on the loop space of the super-double-twisted-torus and its quantization. As a consequence we obtain a rigorous construction of mirror symmetry as an intertwiner of the N=2 super-conformal structures on the super-symmetric sigma-models on the Kodaira-Thurston nilmanifold and a gerby torus of complex dimension 2. As an application we are able to identify global moduli of equivariant generalized complex structures on these target spaces with moduli of equivariant orthogonal complex structures on the doubled geometry.
Cite
@article{arxiv.1512.02258,
title = {On a complex-symplectic mirror pair},
author = {Marco Aldi and Reimundo Heluani},
journal= {arXiv preprint arXiv:1512.02258},
year = {2025}
}