In a conformal field theory in $d$ spacetime dimensions, every local operator has a well-defined dimension (which determines its behaviour under the action of the dilatation operator). An operator of dimension strictly greater than $d$ is called irrelevant, an operator of dimension equal to $d$ is called marginal and an operator of dimension stricly less than $d$ and different from the identity operator is called relevant.
The adjectives relevant and irrelevant describe the effect obtained by perturbing the conformal field theory by one of its local operator and then flowing to the infrared under the renormalization group flow. In particular, the relevant operators are the one which, starting from the given conformal field theory, define perturbations generating non-trivial trajectories of the renormalization group flow.
My question is: what are the known conformal field theories without any relevant operators ?
These particular conformal field theories should play a special role in the "space of quantum field theories" as being the "ultimate end points" of the renormalization group flow.
The only examples I know are:
1) for every spacetime dimension $d$, the trivial conformal field theory, without any local operator different from the identity.
2) for $d=2$, the Monster CFT, which has central charge $c=24$, and whis is an orbifold of the toroidal compactification of 24 free bosons on the Leech lattice (the unique even unimodular lattice of rank 24 without roots). The Monster CFT satisfies holomorphic factorization, the partition function of its holomorphic part is $J(q)=j(q)-744 = 1/q + 196 884 q +...$ (the absence of the term in $q$ is related to the absence of relevant operators) and the Monster group, the greatest sporadic finite group, is its group of global symmetries. The Monster CFT has no relevant operators but also no marginal ones: it is an isolated point in the space of conformal field theories. The Monster CFT is conjecturally the CFT dual of pure gravity on $AdS_3$ at minimal radius (see http://arxiv.org/abs/0706.3359 )
Are there other examples?
One reason why it does not seem easy: if a conformal field theory has a Lagrangian description in terms of massless fields, then turning on masses for all these fields define relevant perturbations and the theory flows in the infrared to the trivial conformal field theory.