Confined Phase In The Real Time Formalism And The Fate Of The World Behind The Horizon

TL;DR

This paper explores the role of type-2 fields in the real time formalism of finite temperature field theories, especially in the confined phase where no black hole horizon exists, proposing they correspond to bulk string fields rather than behind-horizon degrees of freedom.

Contribution

It clarifies the interpretation of type-2 fields in the confined phase, suggesting they represent bulk string fields instead of degrees behind a horizon, contrasting with previous black hole scenarios.

Findings

Type-2 fields do not correspond to behind-horizon degrees in confined phase.

In confined phase, type-2 fields are related to bulk string fields.

The interpretation aligns with the absence of a black hole horizon below the Hawking-Page transition.

Abstract

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.