Effective Actions of Matrix Models on Homogeneous Spaces

TL;DR

This paper computes the effective actions of supersymmetric matrix models on fuzzy S^2×S^2 up to two loops, revealing insights into their large N behavior and dimensionality selection.

Contribution

It provides the first detailed two-loop analysis of supersymmetric matrix models on fuzzy homogeneous spaces, identifying their large N scaling and dimensionality preferences.

Findings

Quantum corrections are O(N) for 4D and O(N^{4/3}) for 6D spaces.

Quantum effects favor 4-dimensionality among fuzzy homogeneous spaces.

The effective actions form consistent solutions of the IIB matrix model.

Abstract

We evaluate the effective actions of supersymmetric matrix models on fuzzy S^2\times S^2 up to the two loop level. Remarkably it turns out to be a consistent solution of IIB matrix model. Based on the power counting and SUSY cancellation arguments, we can identify the 't Hooft coupling and large N scaling behavior of the effective actions to all orders. In the large N limit, the quantum corrections survive except in 2 dimensional limits. They are O(N) and O(N^{4\over 3}) for 4 and 6 dimensional spaces respectively. We argue that quantum effects single out 4 dimensionality among fuzzy homogeneous spaces.