Topological lattice models in four dimensions

Journal Article · Mon Sep 28 00:00:00 EDT 1992 · Modern Physics Letters A; (Singapore)

DOI:https://doi.org/10.1142/S0217732392004171· OSTI ID:6912492

Ooguri, H ^[1]

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1. Kyoto Univ. (Japan). Research Inst. for Mathematical Sciences

In this paper, the authors 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-suymbol 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. The authors 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. 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.

• OSTI ID: 6912492
• Journal Information: Modern Physics Letters A; (Singapore), Vol. 7:30; ISSN 0217-7323
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
STATISTICAL MODELS
MATHEMATICAL MANIFOLDS
ANGULAR MOMENTUM
CORRELATION FUNCTIONS
FOUR-DIMENSIONAL CALCULATIONS
INVARIANCE PRINCIPLES
LATTICE FIELD THEORY
PARTITION FUNCTIONS
RACAH COEFFICIENTS
RECOMBINATION
SU-2 GROUPS
TOPOLOGY
WILSON LOOP
FIELD THEORIES
FUNCTIONS
LIE GROUPS
MATHEMATICAL MODELS
MATHEMATICS
QUANTUM FIELD THEORY
SU GROUPS
SYMMETRY GROUPS
662240* - Models for Strong Interactions- (1992-)