NOTE ON COVARIANT ACTION INTEGRALS IN 3 DIMENSIONS - ART. NO. 104014

We compute, in the saddle point approximation, the partition function for the 2 + 1 black hole using the Gibbons-Hawking approach. Some issu es concerning thr definition of thermodynamical ensembles are clarifie d. It is pointed out that the right action in covariant form is exactl y equal to the Chern-Simons action with no added boundary terms. This action is finite, yields the right canonical free energy and has an ex tremum when the temperature and angular velocity are fixed. The corres pondence with a 1 + 1 CFT is indicated. [S0556-2821(98)08920-6].