Nonabelian Monopoles from Matrices: Seeds of the Spacetime Structure

Abstract

We study the expectation value of (the product) of the one-particle projector (s) in the reduced matrix model and matrix quantum mechanics in general. This quantity is given by the nonabelian Berry phase: we discuss the relevance of this with regard to the spacetime structure. The case of the USp matrix model is examined from this respect. Generalizing our previous work, we carry out the complete computation of this quantity which takes into account both the nature of the degeneracy of the fermions and the presence of the space time points belonging to the antisymmetric representation. We find the singularities as those of the SU(2) Yang monopole connection as well as the pointlike singularities in 9+1 dimensions coming from its SU(8) generalization. The former type of singularities, which extend to four of the directions lying in the antisymmetric representations, may be regarded as seeds of our four dimensional spacetime structure and is not shared by the IIB matrix model. From a mathematical viewpoint, these connections can be generalizable to arbitrary odd space dimensions due to the nontrivial nature of the eigenbundle and the Clifford module structure.

arXiv comment29 pages, Latex, 1 epsf figure

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Cited by in corpus (14)

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• Generalized Monopoles in Six-dimensional Non-Abelian Gauge Theory
• Non-Abelian Self-Dual String Solutions
• The Geometric Phase and Gravitational Precession of D-Branes
• Dynamical Compactification and Inflation in Einstein-Yang-Mills Theory with Higher Derivative Coupling
• Magnetic monopole bibliography
• A Classical Solution in Six-dimensional Gauge Theory with Higher Derivative Coupling
• Matrix Orientifolding and Models with Four or Eight Supercharges
• Finite Energy Monopoles in Non-Abelian Gauge Theories on Odd-dimensional Spaces
• Generalized Self-Duality Equations of Polynomial Type in Yang-Mills Theories
• Orientifolded Matrices and Supersymmetries that Give Rise to Spacetime Directional Asymmetry of Effective Interactions
• Partition Functions of Reduced Matrix Models with Classical Gauge Groups
• The Yang Monopole in IIA Superstring: Multi-charge Disease and Enhancon Cure