QFT on Fuzzy AdS Spaces: Classical Limit and Boundary Correlation Functions

TL;DR

This paper develops quantum field theory on fuzzy anti-de Sitter spaces, analyzing solutions, classical limits, and boundary correlation functions, revealing a two-parameter deformation of conformal two-point functions in low dimensions.

Contribution

It introduces a framework for QFT on fuzzy AdS spaces, solving the Klein-Gordon equation, and deriving boundary two-point functions with new deformations.

Findings

Complete solutions to fuzzy Klein-Gordon equation.

Identification of the classical limit reducing to scalar field modes.

Explicit two-point function in fuzzy AdS$_2$ using Appell function.

Abstract

Quantum field theory on two- and three-dimensional fuzzy anti-de Sitter spaces is introduced and studied. We find a complete set of solutions to the fuzzy Klein-Gordon equation and identify the commutative limit in which they reduce to classical scalar field modes. After introducing the noncommutative boundary via semi-classical states, the fuzzy modes are used to obtain the boundary two-point function. In both two and three dimensions, this gives an interesting two-parameter deformation of the conformal two-point function. For the fuzzy AdS$_2$, the two-point function is given explicitly in terms of the Appell function $F_1$.