Correlators of Matrix Models on Homogeneous Spaces

TL;DR

This paper studies correlators in matrix models on homogeneous spaces like S^2 and S^2 x S^2, revealing geometric insights and scaling behaviors relevant to non-commutative gauge theories.

Contribution

It introduces an efficient method to compute correlators via 1PI diagrams and analyzes their large N scaling, highlighting the fractal structure of fuzzy S^2 x S^2.

Findings

Fuzzy S^2 x S^2 exhibits a 4D fractal structure.

Correlators show logarithmic scaling violations.

Order parameter indicates geometric phase differences.

Abstract

We investigate the correlators of TrA_{mu}A_{nu} in matrix models on homogeneous spaces: S^2 and S^2 x S^2. Their expectation value is a good order parameter to measure the geometry of the space on which non-commutative gauge theory is realized. They also serve as the Wilson lines which carry the minimum momentum. We develop an efficient procedure to calculate them through 1PI diagrams. We determine the large N scaling behavior of the correlators. The order parameter shows that fuzzy S^2 x S^2 acquires a 4 dimensional fractal structure in contrast to fuzzy S^2. We also find that the two point functions exhibit logarithmic scaling violations.