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Coadjoint Orbits, Coycles and Gravitational Wess-Zumino | Anton Alekseev
; Samson L. Shatashvili
; | Date: |
24 Jan 2018 | Abstract: | About 30 years ago, in a joint work with L. Faddeev we introduced a geometric
action on coadjoint orbits. This action, in particular, gives rise to a path
integral formula for characters of the corresponding group $G$. In this paper,
we revisit this topic and observe that the geometric action is a 1-cocycle for
the loop group $LG$. In the case of $G$ being a central extension, we construct
Wess-Zumino (WZ) type terms and show that the cocycle property of the geometric
action gives rise to a Polyakov-Wiegmann (PW) formula. In particular, we obtain
a PW type formula for the Polyakov’s gravitational WZ action. After
quantization, this formula leads to an interesting bulk-boundary decoupling
phenomenon previously observed in the WZW model. We explain that this
decoupling is a general feature of the Wess-Zumino terms obtained from
geometric actions, and that in this case the path integral is expressed in
terms of the 2-cocycle which defines the central extension. In memory of our
teacher Ludwig Faddeev. | Source: | arXiv, 1801.7963 | Services: | Forum | Review | PDF | Favorites |
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