Are there explicit AdS$_3$ soliton solution?
in the sense of Witten's Anti De Sitter Space And Holography and Hawking-Page transition paper, by doing a $$\tau_E, y ,r \to y, \tau_E ,r$$
from a geometry with a Euclidean time $\tau_E$ cigar space and a compactified $y$ circle
to a geometry with a $y$ cigar space and a compactified Euclidean time $\tau_E$ circle
If yes, with a AdS3 soliton solution, what are the form of solutions?
If not, without a AdS3 soliton solution, what are the obstructions?