Quantizing field theories in noncommutative geometry and the correspondence between anti de Sitter space and conformal field theory

TL;DR

This paper explores the application of non-commutative geometry to quantize field theories on two-layer AdS spaces, revealing a logarithmic conformal field theory at the boundary via the AdS/CFT correspondence, thus proposing a novel approach to quantum field theory.

Contribution

It introduces a method to study spinors and scalars in non-commutative two-layer AdS spaces and establishes a connection to logarithmic conformal field theories at the boundary.

Findings

Logarithmic conformal field theory arises at the boundary of two-layer AdS space.

Non-commutative geometry provides a framework for quantizing field theories in curved spacetime.

A new approach to quantum field theory via non-commutative geometry is proposed.

Abstract

By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS$_{d+1}$ space. We have found that in the boundary of two layers AdS$_{d+1}$ space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry.