Large N optimization for multi-matrix systems

In this work we revisit the problem of solving multi-matrix systems through numerical large $N$ methods. The framework is a collective, loop space representation which provides constrained optimization problem, addressed master-field minimization. This scheme applies both to integrals ($c=0$ systems) and quantum mechanics ($c=1$). complete fluctuation spectrum also computable in above scheme, immediate physical relevance later case. complexity (and growth degrees freedom) at have stymied earlier attempts present significant improvements regard. (constrained) minimization calculations are easily achieved with close $10^4$ variables, giving solution Migdal-Makeenko, collective field equations. Considering number dynamical (loop) variables extreme nonlinearity high precision obtained when confronted solvable cases. Through results presented, prove that our solves, by methods, general two matrix model problem.