  We describe new conformal field theories based on symplectic fermions that
can be extrapolated between 2 and 4 dimensions. The critical exponents depend
continuously on the number of components N of the fermions and the dimension D.
In the context of anti-ferromagnetism, the N=2 theory is proposed to describe a
deconfined quantum critical spin liquid corresponding to a transition between a
Neel ordered phase and a VBS-like phase.
