Abstract
The high-temperature or small compactification scales phase of closed string is studied in the 2+1 terms of the open topological membrane theory. The main feature of this phase is the breaking of the world-sheet conformal symmetry due to the Berezinsky- Kosterlitz-Thouless (BKT) phase transition. From the 2+1 point of view this breaking corresponds to the spontaneous breaking of the gauge symmetry of the topologically massive gauge theory (TMGT), which leads to the disappearing of the string's degree of freedom from the membrane boundary (string world-sheet). This spontaneous breaking of the gauge symmetry is nothing but the superconducting phase transition inside the membrane. The possible mechanism of this transition is considered and the connection with anyonic superconductivity is discussed, as well as the description of the world-sheet vortices in 2+1 terms as the charged vortices (flux tubes) in the abelian TMGT+Higgs model.
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