Mirror Symmetry of elliptic curves and Ising Model
نویسنده
چکیده
We study the differential equations governing mirror symmetry of elliptic curves, and obtain a characterization of the ODEs which give rise to the integral q-expansion of mirror maps. Through theta function representation of the defining equation, we express the mirror correspondence in terms of theta constants. By investigating the elliptic curves in X9-family, the identification of the Landau-Ginzburg potential with the spectral curve of Ising model is obtained. Through the Jacobi elliptic function parametrization of Boltzmann weights in the statistical model, an exact Jacobi form-like formula of mirror map is described . Supported in part by the NSC grant of Taiwan.
منابع مشابه
Mirror Symmetry and Elliptic Curves
I review how recent results in quantum eld theory con-rm two general predictions of the mirror symmetry program in the special case of elliptic curves: (1) counting functions of holomorphic curves on a Calabi-Yau space (Gromov-Witten invariants) arèquasi-modular forms' for the mirror family; (2) they can be computed by a summation over trivalent Feynman graphs.
متن کاملpreliminary draft November 15 , 2002 Mirror Symmetry and Elliptic Curves ∗
I review how recent results in quantum field theory confirm two general predictions of the mirror symmetry program in the special case of elliptic curves: (1) counting functions of holomorphic curves on a CalabiYau space (Gromov-Witten invariants) are ‘quasi-modular forms’ for the mirror family; (2) they can be computed by a summation over trivalent Feynman graphs. ∗To be published in The Modul...
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