Covariant Field Equations, Gauge Fields and Conservation Laws from Yang-Mills Matrix Models

TL;DR

This paper derives covariant field equations and conservation laws for gauge and scalar fields on noncommutative branes within Yang-Mills matrix models, highlighting their quantum stability and geometric implications.

Contribution

It provides a derivation of covariant field equations from matrix models and shows their protection from quantum corrections, extending the understanding of gauge fields in noncommutative geometry.

Findings

Derived covariant equations from matrix models.

Showed equations are protected from quantum corrections.

Discussed effective metrics on noncommutative space-times.

Abstract

The effective geometry and the gravitational coupling of nonabelian gauge and scalar fields on generic NC branes in Yang-Mills matrix models is determined. Covariant field equations are derived from the basic matrix equations of motions, known as Yang-Mills algebra. Remarkably, the equations of motion for the Poisson structure and for the nonabelian gauge fields follow from a matrix Noether theorem, and are therefore protected from quantum corrections. This provides a transparent derivation and generalization of the effective action governing the SU(n) gauge fields obtained in [1], including the would-be topological term. In particular, the IKKT matrix model is capable of describing 4-dimensional NC space-times with a general effective metric. Metric deformations of flat Moyal-Weyl space are briefly discussed.