Extended T-Duality In Three Dimensions

The concept of Wick duality of General Relativity in 2 + 1 dimensions with a cosmological constant is extended to the low energy effective action of bosonic string theory in 2 + 1 dimensions. We call this extension stringly Wick duality and we show that it is a symmetry of the low energy effective action. The structure of this duality is studied by composing it with the Buscher duality along a time-like killing vector of the nonrotating BTZ Black Hole solution, and it is proved that the action of both dualities commutates. Given the topological nature of string theory in three dimensions, it is argued that the stringly Wick duality must be an exact symmetry of the entire theory.