Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-12-30
J.Exp.Theor.Phys.111:375-383,2010
Physics
High Energy Physics
High Energy Physics - Theory
LaTex, 14 pages, some acknowledgments added
Scientific paper
10.1134/S1063776110090062
The geometry of $k^{K}$ Gepner model, where $k+2=2K$ is investigated by free-field representation known as "$bc\bet\gm$"-system. Using this representation it is shown directly that internal sector of the model is given by Landau-Ginzburg $\mathbb{C}^{K}/\mathbb{Z}_{2K}$-orbifold. Then we consider the deformation of the orbifold by marginal anti-chiral-chiral operator. Analyzing the holomorphic sector of the deformed space of states we show that it has chiral de Rham complex structure of some toric manifold, where toric dates are given by certain fermionic screening currents. It allows to relate the Gepner model deformed by the marginal operator to the $\sigma$-model on CY manifold realized as double cover of $\mathbb{P}^{K-1}$ with ramification along certain submanifold.
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