Convergent Yang-Mills Matrix Theories

TL;DR

This paper analyzes the convergence properties of partition functions and correlation functions in bosonic and supersymmetric Yang-Mills matrix models across various dimensions and gauge groups, with implications for string theory models.

Contribution

It extends previous results by determining convergence criteria for partition and correlation functions in bosonic and supersymmetric Yang-Mills matrix models for different gauge groups and dimensions.

Findings

Supersymmetric models converge in D=4,6,10.

Bosonic models converge for D above a critical dimension D_c.

Results imply convergence of the IKKT IIB string matrix model.

Abstract

We consider the partition function and correlation functions in the bosonic and supersymmetric Yang-Mills matrix models with compact semi-simple gauge group. In the supersymmetric case, we show that the partition function converges when $D=4,6$ and 10, and that correlation functions of degree $k< k_c=2(D-3)$ are convergent independently of the group. In the bosonic case we show that the partition function is convergent when $D \geq D_c$, and that correlation functions of degree $k < k_c$ are convergent, and calculate $D_c$ and $k_c$ for each group, thus extending our previous results for SU(N). As a special case these results establish that the partition function and a set of correlation functions in the IKKT IIB string matrix model are convergent.