It is well known that 2D Ising model at critical point can be described by a 2D CFT. The CFT is identical to free Majorana fermions. It has three primary operators namely
The identity.
The Ising spin $\sigma$ with weight $(1/16, 1/16)$.
The energy density $\epsilon$ with weight $(1/2, 1/2)$.
As far as I understand these are global i.e, $SL(2,R)$ primaries. But 2D CFTs have larger symmetry group - Virasoro group. What are those Virasoro primaries?
The three fields that you mention are indeed Virasoro primaries, i.e. they are eigenvectors of the Virasoro generators $L_0,\bar L_0$ and are killed by $L_{n>0},\bar L_{n>0}$. Therefore they are also $SL(2)$ primaries (in other words quasi-primaries), because in particular they are killed by $L_1, \bar L_1$, i.e. by those Virasoro annihilation modes that belong to the Lie algebra of $SL(2)$. These three fields are the only Virasoro primary fields in the model. However, there exist infinitely many other $SL(2)$ primary fields, because a number of Virasoro descendent fields are killed by $L_1,\bar L_1$ (but not by $L_{n>1},\bar L_{n>1}$).
In other words, there are fewer primary fields with respect to the larger algebra (Virasoro) than with respect to its subalgebra ($SL(2)$).
