Abstract
In this note we point out that the one-loop partition function of threedimensional flat gravity, computed along the lines originally developed for the anti-de Sitter case, reproduces characters of the BMS3 group.
Highlights
There are several ways to compute S(0) from the classical action, including boundary terms
In other words, requiring a well defined variational principe and a finite on-shell action for a class of spacetimes does not fix the ambiguity that consists in adding a finite combination of the quantities that are held fixed in the variational principle
One can use the fact that three-dimensional gravity has no local degrees of freedom to understand the nature of the quantum corrections S(i) to this classical action, following [2]
Summary
There are several ways to compute S(0) from the classical action, including boundary terms. One loop partition function of three-dimensional flat gravity This is the only contribution and the on-shell action is automatically finite. In order to make the classical part of the partition function invariant under the analog of modular S-transformations in the flat case [14, 15]
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