2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121751We 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.21 pages, version 2: expanded discussion on possible applications to superconductivity, which shows a two-band theory with some BCS-like pairing interactions; a few references added, typos corrected, version 3: minor changes, version submitted for publication to JSTAT. version 4: For sake of clarity, this version focuses only on possible applications to deconfined quantum criticality; all the Ising model discussion is contained in cond-mat/0610817Strongly Correlated ElectronsDisordered Systems and Neural NetworksHigh Energy Physics - LatticeHigh Energy Physics - Theorytext