Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2009-08-07
JHEP 0909:073,2009
Physics
High Energy Physics
High Energy Physics - Theory
21 pages, 1 figure. v2 is the final version and has a few minor changes
Scientific paper
10.1088/1126-6708/2009/09/073
An unambiguous definition of Feynman amplitudes in the Wess-Zumino-Witten sigma model and the Chern-Simon gauge theory with a general Lie group is determined by a certain geometric structure on the group. For the WZW amplitudes, this is a (bundle) gerbe with connection of an appropriate curvature whereas for the CS amplitudes, the gerbe has to be additionally equipped with a multiplicative structure assuring its compatibility with the group multiplication. We show that for simple compact Lie groups the obstruction to the existence of a multiplicative structure is provided by a 2-cocycle of phases that appears in the Polyakov-Wiegmann formula relating the Wess-Zumino action functional of the product of group-valued fields to the sum of the individual contributions. These phases were computed long time ago for all compact simple Lie groups. If they are trivial, then the multiplicative structure exists and is unique up to isomorphism.
Gawedzki Krzysztof
Waldorf Konrad
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