TRANSVERSE LATTICE CONSTRUCTION OF 2+1 CHERN-SIMONS THEORY

7 March 1992

journal article
Published by World Scientific Pub Co Pte Ltd in Modern Physics Letters A

Vol. 7 (7) , 601-610
https://doi.org/10.1142/s0217732392000574

Abstract

A transverse lattice model, with one lattice dimension and two continuum dimensions, is constructed by introducing Wess-Zumino terms into the gauged (1+1)-dimensional nonlinear sigma model action of the link fields. Its continuum limit is the pure Chern-Simons gauge theory in 2+1 dimensions. The lattice model is quantized, and some simple expectation values for Wilson loops on M²×S¹ are evaluated. This construction provides an explicit connection between Chern-Simons theory and the gauged Wess-Zumino-Witten model.

Keywords

GAUGE THEORY
THREE DIMENSIONAL
LATTICE MODEL
MATHEMATICAL MODEL
INVARIANCE PRINCIPLE
ELEMENTARY PARTICLES
CHERN SIMONS
EXPECTED VALUE
CHERN SIMONS THEORY
GAUGE INVARIANCE
QUANTUM FIELD THEORY
LATTICE FIELD THEORY

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