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In the real time formulation of finite temperature field theories, oneintroduces an additional set of fields (type-2 fields) associated to each fieldin the original theory (type-1 field). In hep-th/0106112, in the context of theAdS-CFT correspondence, Maldacena interpreted type-2 fields as living on aboundary behind the black hole horizon. However, below the Hawking-Pagetransition temperature, the thermodynamically preferred configuration is thethermal AdS without a black hole, and hence there are no horizon and boundarybehind it. This means that when the dual gauge theory is in confined phase, thetype-2 fields cannot be associated with the degrees of freedom behind the blackhole horizon. I argue that in this case the role of the type-2 fields is tomake up bulk type-2 fields of classical closed string field theory on AdS atfinite temperature in the real time formalism.Comment: v2: cases divided into sections with more detailed explanations.  considerably enlarged with examples and a lot of figures. sec 4.1.2 for  general closed cut-out circuits and appendix A for a sample calculation newly  added. many minor corrections and clarifying comments. refs added. v3: refs  and related discussion added. 1+46 pages, 26 figures. published versio

Confined phase in the real time formalism and the fate of the world behind the horizon