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Topological Lattice Models in Four Dimensions

Ooguri, Hirosi (1992) Topological Lattice Models in Four Dimensions. Modern Physics Letters A, 7 (30). pp. 2799-2810. ISSN 0217-7323. doi:10.1142/S0217732392004171.

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We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G=SU(2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. The q-analog of the model is also constructed, and it is argued that its partition function is invariant under the Alexander moves. It is discussed how to realize the 't Hooft operator in these models associated to a closed surface in four dimensions as well as the Wilson operator associated to a closed loop. Correlation functions of these operators in the q-deformed version of the model would define a new type of invariants of knots and links in four dimensions.

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Ooguri, Hirosi0000-0001-6021-3778
Additional Information:© 1992 World Scientific Publishing. Received: 3 June 1992. Dedicated to Professors Huzihiro Araki and Noboru Nakanishi on the occasion of their sixtieth birthdays. I would like to thank T. Eguchi, K. Higashijima, T. Inami, N. Ishibashi, Y. Yamada, S. Yahikozawa and T. Yoneya for discussions. I would also like to thank the members of the theory group in KEK, where part of this work was done, for their hospitality.
Issue or Number:30
Record Number:CaltechAUTHORS:20161220-155721883
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Official Citation:TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS HIROSI OOGURI Modern Physics Letters A 1992 07:30, 2799-2810
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73017
Deposited By: George Porter
Deposited On:21 Dec 2016 15:36
Last Modified:11 Nov 2021 05:10

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