Free-field representations and geometry of some Gepner models
The geometry of the kK Gepner model, where k + 2 = 2K, is investigated by a free-field representation known as the “bcβγ” system. Using this representation, we directly show that the internal sector of the model is given by Landau-Ginzburg ℂK/ℤ2K orbifold. Then we consider the deformation of the orbifold by a marginal antichiral-chiral operator. Analyzing the chiral de Rham complex structure in the holomorphic sector, we show that it coincides with chiral de Rham complex of some toric manifold, where toric data are given by certain fermionic screening currents. This allows relating the Gepner model deformed by the marginal operator to a σ-model on the CY manifold realized as a double cover of ℙK − 1 with ramification along a certain submanifold.
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