Nodes as Composite Operators in Matrix Models 1

Riemann surfaces with nodes can be described by introducing simple composite operators in matrix models. In the case of the Kontsevich model, it is sufficient to add the quadratic, but “non-propagating”, term (tr[X]) to the Lagrangian. The corresponding JenkinsStrebel differentials have pairwise identified simple poles. The result is in agreement with a conjecture formulated by Kontsevich and recently investigated by Arbarello and Cornalba that the setMm∗,s of ribbon graphs with s faces andm∗ = (m0, m1, . . . , mj , . . .) vertices of valencies (1, 3, . . . , 2j + 1, . . .) “can be expressed in terms of Mumford-Morita classes”: one gets an interpretation for univalent vertices. I also address the possible relationship with a recently formulated theory of constrained topological gravity.