Effective Actions of IIB Matrix Model on S^3

TL;DR

This paper studies the effective actions of a deformed IIB matrix model on S^3, revealing the divergence behavior at different loop levels and suggesting higher loops are cutoff-insensitive due to super renormalizability.

Contribution

It demonstrates the realization of S^3 in a deformed IIB matrix model and analyzes the divergence structure of the effective action at various loop levels.

Findings

Tree and one-loop divergences are UV-sensitive.

Two-loop contributions are only logarithmically divergent.

Higher loops are expected to be cutoff-insensitive due to super renormalizability.

Abstract

S^3 is a simple principle bundle which is locally S^2 \times S^1. It has been shown that such a space can be constructed in terms of matrix models. It has been also shown that such a space can be realized by a generalized compactification procedure in the S^1 direction. We investigate the effective action of supersymmetric gauge theory on S^3 with an angular momentum cutoff and that of a matrix model compactification. The both cases can be realized in a deformed IIB matrix model with a Myers Term. We find that the highly divergent contributions at the tree and one loop level are sensitive to the uv cutoff. However the two loop level contributions are universal since they are only logarithmically divergent. We expect that the higher loop contributions are insensitive to the uv cutoff since 3d gauge theory is super renormalizable.