Fuzzy Spheres in AdS/CFT Correspondence and Holography from Noncommutativity

TL;DR

This paper explores fuzzy sphere models within the AdS/CFT framework, linking noncommutative geometry to holography, and proposes models that explain stringy exclusion and UV/IR phenomena.

Contribution

It introduces fuzzy S^2 and S^4 models as natural quantum geometries in AdS/CFT and connects them to the dipole mechanism and holographic principles.

Findings

Fuzzy S^2 and S^4 models fit the data from the stringy exclusion principle.

Wrapped fractional membranes account for large ground state degeneracy in AdS_2 x S^2.

A fuzzy AdS_2 model may explain the UV/IR connection.

Abstract

We show that the existent fuzzy S^2 and S^4 models are natural candidates for the quantum geometry on the corresponding spheres in AdS/CFT correspondence. These models fit nicely the data from the dipole mechanism for the stringy exclusion principle. In the AdS_2 X S^2 case, we show that a wrapped fractional membrane can be used to count for the large ground state degeneracy. We also propose a fuzzy AdS_2 model whose fundamental commutation relation may underlie the UV/IR connection.