Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral

  • Massimo Porrati
  • Cedric YuEmail author
Open Access
Regular Article - Theoretical Physics


We evaluate to one loop the functional integral that computes the partition functions of Chern-Simons theories based on compact groups, using the background field method and a covariant gauge fixing. We compare our computation with the results of other, less direct methods. We find that our method correctly computes the characters of irreducible representations of Kac-Moody algebras. To extend the computation to non-compact groups we need to perform an appropriate analytic continuation of the partition function of the compact group. Non-vacuum characters are found by inserting a Wilson loop in the functional integral. We then extend our method to Euclidean Anti-de Sitter pure gravity in three dimensions. The explicit computation unveils several interesting features and lessons. The most important among them is that the very definition of gravity in the first-order Chern-Simons formalism requires non-trivial analytic continuations of the gauge fields outside their original domains of definition.


Chern-Simons Theories Conformal and W Symmetry Wilson, ’t Hooft and Polyakov loops AdS-CFT Correspondence 


Open Access

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© The Author(s) 2019

Authors and Affiliations

  1. 1.Center for Cosmology and Particle Physics, Department of PhysicsNew York UniversityNew YorkU.S.A.

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