  Simplest examples of AdS/CFT duality correspond to free CFTs in d dimensions
with fields in vector or adjoint representation of an internal symmetry group
dual in the large N limit to a theory of massless or massless plus massive
higher spins in AdS_{d+1}. One may also study generalizations when conformal
fields belong to higher dimensional representations, i.e. carry more than two
internal symmetry indices. Here we consider the case of the 3-fundamental
("3-plet") representation. One motivation is a conjectured connection to
multiple M5-brane theory: heuristic arguments suggest that it may be related to
an (interacting) CFT of 6d (2,0) tensor multiplets in 3-plet representation of
large N symmetry group that has an AdS_7 dual. We compute the singlet partition
function Z on S^1 x S^{d-1} for a free field in 3-plet representation of U(N)
and analyse its novel large N behaviour. The large N limit of the low
temperature expansion of Z which is convergent in the vector and adjoint cases
here is only asymptotic, reflecting the much faster growth of the number of
singlet operators with dimension, indicating a phase transition at very low
temperature. Indeed, while the critical temperatures in the vector (T_c ~ N^a,
a >0) and adjoint (T_c ~ 1) cases are finite, we find that in the 3-plet case
T_c ~ 1/ log N, i.e. it approaches zero at large N. We discuss some details of
large N solution for the eigenvalue distribution. Similar conclusions apply to
higher p-plet representations of U(N) or O(N) and also to the free p-tensor
theories invariant under [U(N)]^p or [O(N)]^p starting with p=3.
