We consider large-N multi-matrix models whose action closely mimics that of
Yang-Mills theory, including gauge-fixing and ghost terms. We show that the
factorized Schwinger-Dyson loop equations, expressed in terms of the generating
series of gluon and ghost correlations G(xi), are quadratic equations S^i G = G
xi^i G in concatenation of correlations. The Schwinger-Dyson operator S^i is
built from the left annihilation operator, which does not satisfy the Leibnitz
rule with respect to concatenation. So the loop equations are not differential
equations. We show that left annihilation is a derivation of the graded shuffle
product of gluon and ghost correlations. The shuffle product is the point-wise
product of Wilson loops, expressed in terms of correlations. So in the limit
where concatenation is approximated by shuffle products, the loop equations
become differential equations. Remarkably, the Schwinger-Dyson operator as a
whole is also a derivation of the graded shuffle product. This allows us to
turn the loop equations into linear equations for the shuffle reciprocal, which
might serve as a starting point for an approximation scheme.Comment: 13 pages, added discussion & references, title changed, minor
corrections, published versio