Parity Violating Marginal Deformation of the 3D Gross-Neveu-Thirring Model

A hybrid of the critical three dimensional Gross-Neveu and Thirring models deformed by explicit parity breaking operators is studied in the large N expansion and using the renormalization group. The regime of coupling constants where the theory is stable is identified and criteria for the occurrence of fixed points in that regime are found. For a certain range of Chern-Simons level, we find stable charge-gapped phase with spontaneously broken approximate scale invariance and a parametrically light dilaton. The Chern-Simons level can be tuned to the stability edge resulting in exact scale invariance which is spontaneously broken, accompanied by a massless dilaton. For another, narrow range of Chern-Simons levels we find a conformal window where the theory flows to a Wilson-Fisher-like fixed point and is a novel (and rare) example of a non-supersymmetric non-trivial parity and time reversal violating three dimensional conformal field theory with scalar, spinor and vector fields.