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Coadjoint Orbits, Coycles and Gravitational Wess-Zumino

Anton Alekseev, Samson L. Shatashvili

24/1/18 Published in : arXiv:1801.07963

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.

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Phase I & II research project(s)

  • Field Theory
  • Geometry, Topology and Physics

On the number of maximal paths in directed last-passage percolation

The Bulk-Edge Correspondence for Disordered Chiral Chains

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The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

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