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The General O(n) Quartic Matrix Model and Its Application to Counting Tangles and Links

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Abstract:

 The counting of alternating tangles in terms of their crossing number, number of external legs and connected components is presented here in a unified framework using quantum field-theoretic methods applied to a matrix model of colored links. The overcounting related to topological equivalence of diagrams is removed by means of a renormalization scheme of the matrix model; the corresponding ``renormalization equations'' are derived. Some particular cases are studied in detail and solved exactly.

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  1. Laboratoire de Physique Théorique et Modèles Statistiques, Université Paris-Sud, Bâtiment 100, 91405 Orsay Cedex, France, , , , , , FR

    P. Zinn-Justin

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  1. P. Zinn-Justin
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Received: 8 August 2001 / Accepted: 27 January 2003 Published online: 5 May 2003

Communicated by R. H. Dijkgraaf

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Zinn-Justin, P. The General O(n) Quartic Matrix Model and Its Application to Counting Tangles and Links. Commun. Math. Phys. 238, 287–304 (2003). https://doi.org/10.1007/s00220-003-0846-0

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  • DOI: https://doi.org/10.1007/s00220-003-0846-0

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