ar X iv : h ep - t h / 05 10 05 6 v 3 1 8 Fe b 20 06 Confined Phase In The Real Time Formalism And The Fate

In the real time formulation of finite temperature field theories, one introduces an additional set of fields (type-2 fields) associated to each field in the original theory (type-1 field). In [1], in the context of the AdS-CFT correspondence, Maldacena interpreted type-2 fields as living on a boundary behind the black hole horizon. However, below the Hawking-Page transition temperature, the thermodynamically preferred configuration is the thermal AdS without a black hole, and hence there are no horizon and boundary behind it. This means that when the dual gauge theory is in confined phase, the type-2 fields cannot be associated with the degrees of freedom behind the black hole horizon. I argue that in this case the role of the type-2 fields is to make up bulk type-2 fields of classical closed string field theory on AdS at finite temperature in the real time formalism.