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

TL;DR

This paper derives exact solutions for massless scalars and spinors on quantized Euclidean AdS_2 and uses the AdS/CFT correspondence to compute boundary correlation functions, showing quantization does not break boundary conformal symmetry.

Contribution

It provides the first exact solutions for fields on quantized AdS_2 and demonstrates that boundary conformal symmetry remains intact under bulk quantization.

Findings

Quantization does not spoil boundary conformal symmetry.

Bulk quantization rescales scalar two-point functions.

Spinor two-point functions remain unaffected by quantization.

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.