Geometry of Reduced Supersymmetric 4D Yang-Mills Integrals

TL;DR

This paper numerically investigates the geometric properties of reduced supersymmetric 4D Yang-Mills integrals, revealing spontaneous symmetry breaking and one-dimensional configurations at large eigenvalues, with implications for the IKKT model.

Contribution

It provides the first detailed numerical analysis of the geometric structure and symmetry breaking in reduced supersymmetric 4D Yang-Mills integrals for various N.

Findings

Spontaneous breaking of rotational symmetry at large eigenvalues.

Dominance of one-dimensional configurations in the studied regime.

Insights into the geometric nature of the IKKT model.

Abstract

We study numerically the geometric properties of reduced supersymmetric non-compact SU(N) Yang-Mills integrals in D=4 dimensions, for N = 2,3, ..., 8. We show that in the range of large eigenvalues of the matrices A^mu, the original D-dimensional rotational symmetry is spontaneously broken and the dominating field configurations become one-dimensional, as anticipated by studies of the underlying surface theory. We also discuss possible implications of our results for the IKKT model.