  This paper explores the conjecture that large Nc gauge theories have a
Hagedorn spectrum, if, and only if, they are confining and posses an explicit
or emergent center symmetry. Evidence in support of this conjecture is
presented. Many classes of large Nc gauge theories are considered. In all
cases, we find that theories for which there exists a strong plausibility
argument for a Hagedorn spectrum at large Nc are also believed to be confining
and possess either an explicit center symmetric or have a strong plausibility
argument for the existence of an emergent center symmetry at large Nc .
Conversely, all theories we considered which are believed not to have a
Hagedorn spectrum at large Nc, either were known not to be confining or else
were believed to lack an emergent center symmetry. This is consistent with
expectations based on the conjecture.
