  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 hep-th/0106112, 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.
