Abstract
We consider large
N zero-coupling
d-dimensional
U
(
N
)
gauge theories, with
N
f
matter fields in the fundamental representation on a compact spatial manifold
S
d
−
1
×
time, with
N
f
/
N
finite. The Gauss' law constraint induces interactions among the fields, in spite of the zero-coupling. This class of theories undergo a 3rd order deconfinement phase transition at a temperature
T
c
proportional to the inverse length scale of the compact manifold. The low-temperature phase has a free-energy of
O
(
N
f
2
)
, interpreted as that of a gas of (color singlet) mesons and glueballs. The high-temperature (deconfinement) phase has a free energy of order
N
2
f
(
N
f
/
N
,
T
)
, which is interpreted as that of a gas of gluons and of fundamental and anti-fundamental matter states. This suggests the existence of a dual string theory, and a transition to a black hole at high temperature.