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

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.

31 pages. V2: minor corrections, references added

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• An extended standard model and its Higgs geometry from the matrix model
• On the 1-loop effective action for the IKKT model and non-commutative branes
• Gauge Theories on Deformed Spaces
• Schwarzschild Geometry Emerging from Matrix Models
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• Curvature and Gravity Actions for Matrix Models
• IR Dynamics from UV Divergences: UV/IR Mixing, NCFT, and the Hierarchy Problem
• On the Newtonian limit of emergent NC gravity and long-distance corrections
• Gravity and compactified branes in matrix models
• Tensor calculus on noncommutative spaces
• Heat kernel expansion and induced action for the matrix model Dirac operator
• On Poisson geometries related to noncommutative emergent gravity
• Comparing Quantum Gravity Models: String Theory, Loop Quantum Gravity, and Entanglement gravity versus $SU(\infty )$-QGR
• The curvature of branes, currents and gravity in matrix models
• Fermions and noncommutative emergent gravity II: Curved branes in extra dimensions
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Translation-Invariant Noncommutative Gauge Theories, Matrix Modeling and Noncommutative Geometry
• Fermions Coupled to Emergent Noncommutative Gravity