Critical Fermions with Spontaneously Broken Scale Symmetry

We study relativistic fermions in three euclidean dimensions with four- and six-fermion interactions of the Gross-Neveu type. In the limit of many fermion flavors, and besides the isolated free fixed point, the theory displays a line of interacting ultraviolet fixed points. At the endpoint of the critical line, we establish that mass is generated through the spontaneous breaking of quantum scale invariance. Curiously, broken parity symmetry is a prerequisite for the spontaneous generation of mass rather than a consequence thereof. We also calculate critical exponents and find that hyperscaling relations are violated. Further similarities with critical scalar theories, and implications for conformal field theories and higher spin theories are discussed.