Coadjoint Orbits, Cocycles and Gravitational Wess-Zumino
| Autor: | Alekseev, Anton, Shatashvili, Samson L. |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1142/S0129055X18400019 |
| Popis: | 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. Comment: 15 pages, v2: references added |
| Databáze: | arXiv |
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