Nodes as Composite Operators in Matrix Models

Details Nodes as Composite Operators in Matrix Models Nodes as Composite Operators in Matrix Models

1994-11-28

arxiv.org/abs/hep-th/9411206v2

Class.Quant.Grav.12:1135-1150,1995

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1088/0264-9381/12/5/005

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 ${\cal M}_{m*,s}$ of ribbon graphs with s faces and $m*=(m_0,m_1,\ldots,m_j,\ldots)$ vertices of valencies $(1,3,\ldots,2j+1,\ldots)$ ``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.

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