Nodes as Composite Operators in Matrix Models

Abstract

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])^2 to the Lagrangian. The corresponding Jenkins-Strebel 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 set ${\mathcal{M}}_{m\ast ,s}$ of ribbon graphs with s faces and $m\ast =(m_0,m_1,\dots ,m_j,\dots )$ vertices of valencies $(1,3,\dots ,2j+1,\dots )$ ``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.

22 pages, latex, 1+5 figures. 1 figure available on request

References in corpus (4)

• Combinatorial and algebro-geometric cohomology classes on the moduli spaces of curves
• Polynomial averages in the Kontsevich model
• Constrained Topological Field Theory
• Constrained Topological Gravity from Twisted N=2 Liouville Theory

Cited by in corpus (1)

• Handling Handles. Part II. Stratification and Data Analysis