Name of fermionic CFT theory I'm looking for a name or references to theories that include a stress energy tensor of the form
$$T(z)=A:\phi^\alpha\partial\phi_\alpha:(z)+B:\prod_{i=1}^{D}\phi^i:(z)$$
$\alpha=1,...,D$. 
Where the fields anti-commute. In particular I'd like to know what kind sensible operators can be formed from normal ordered products of the $\phi$
Edit
As commented below, my main interest is $D=4$ and from my calculations it seems that most of the operators than can be formed are only sensible when $B=0$ and there's only one type of operators (of weight 1) that can be formed when $B\neq 0$.
 A: When you talk about CFTs, it's clear that a theory of this form may only be a CFT, conformal, when $D=4$ because the stress-energy tensor must have dimension 2 which you may only get from 4 fermions that have $h=1/2$ each, and they do as manifested by the first term.
At least an example of a theory with a quartic term in the fermions is known as the Thirring model, and it may be bosonized (is equivalent) to the sine-Gordon model, see e.g.

http://www.kph.tuwien.ac.at/element/equival/

Even if you meant the IR fixed point of a more general theory with a more general $D$, it's clear that $D$ must be even (superselection sectors, Grassmann segregation) and there are additional constraints.
Let me mention that even for $D=4$, if you write the product of components in the quartic term differently from the Thirring model, you will get a theory that may look conformal at the classical level but it won't be conformal quantum mechanically. The conformality of a theory is an extremely constraining condition. One can't expect that whatever we write down is conformal.
