Stability of fuzzy $S^2 \times S^2$ geometry in IIB matrix model

TL;DR

This paper investigates the stability of fuzzy $S^2 imes S^2$ geometries within the IIB matrix model, analyzing size asymmetries, effective action scaling, and the preference for symmetric configurations at two loops.

Contribution

It identifies the all-order scaling behavior of the effective action and introduces a new method for evaluating amplitudes on fuzzy $S^2 imes S^2$.

Findings

Symmetric $S^2 imes S^2$ is favored at two loops.

Effective action scaling is determined to all orders.

A new approach for amplitude evaluation on fuzzy geometries.

Abstract

We continue our study of the IIB matrix model on fuzzy $S^2 \times S^2$. Especially in this paper we focus on the case where the size of one of $S^2\times S^2$ is different from the other. By the power counting and SUSY cancellation arguments, we can identify the 't Hooft coupling and large $N$ scaling behavior of the effective action to all orders. We conclude that the most symmetric $S^2 \times S^2$ configuration where the both $S^2$s are of the same size is favored at the two loop level. In addition we develop a new approach to evaluate the amplitudes on fuzzy $S^2 \times S^2$.