Chern-Simons theory for compact non-semisimple Lie groups

T. P. Killingback

doi:10.1088/0264-9381/7/12/004

Chern-Simons theory for compact non-semisimple Lie groups

T. P. Killingback

Mathematics

CERN

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Abstract

The author defines Chern-Simons theory (CS) for the compact non-semisimple group U(n). Quantum CS theory for a U(n) gauge bundle of degree r is related to the representation theory of the rth component of the loop group of U(n). The representations of the loop group of U(n) which feature in the quantum CS theory are also considered from the viewpoint of geometric quantization of the U(n) WZW model.

Original language	English
Article number	004
Pages (from-to)	2179-2193
Number of pages	15
Journal	Classical and Quantum Gravity
Volume	7
Issue number	12
DOIs	https://doi.org/10.1088/0264-9381/7/12/004
State	Published - 1990

ASJC Scopus Subject Areas

Physics and Astronomy (miscellaneous)

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10.1088/0264-9381/7/12/004

Cite this

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abstract = "The author defines Chern-Simons theory (CS) for the compact non-semisimple group U(n). Quantum CS theory for a U(n) gauge bundle of degree r is related to the representation theory of the rth component of the loop group of U(n). The representations of the loop group of U(n) which feature in the quantum CS theory are also considered from the viewpoint of geometric quantization of the U(n) WZW model.",

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AB - The author defines Chern-Simons theory (CS) for the compact non-semisimple group U(n). Quantum CS theory for a U(n) gauge bundle of degree r is related to the representation theory of the rth component of the loop group of U(n). The representations of the loop group of U(n) which feature in the quantum CS theory are also considered from the viewpoint of geometric quantization of the U(n) WZW model.

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Chern-Simons theory for compact non-semisimple Lie groups

Abstract

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