Exact solutions for scalars and spinors on quantized (Euclidean) $AdS_2$ and the correspondence principle

Abstract

We obtain the exact solutions to the field equations for massless scalar and massless spinor fields on quantized two-dimensional anti-de Sitter space. We then apply the AdS/CFT correspondence principle to get exact answers for the two point correlation functions of the associated operators on the boundary. The results support the conclusion that conformal symmetry on the boundary is not spoiled by quantization of the bulk. Moreover, quantization of the bulk has no effect on the spinor two-point correlation function, while it induces an overall re-scaling in the scalar two-point correlation function.