CP^(N-1) models and the Quantized 2D Black Holes

We have examined the coupled system of the dilaton gravity and the $CP^{N-1}$ theory known as a model of the confinement of massive scalar quarks. After the quantization of the system, we could see the quantum effect of the gravitation on the coupling constant of $CP^{N-1}$ model and how the coupling constant of dynamically induced gauge field changes near the black hole configuration.