Critical Fermions with Spontaneously Broken Scale Symmetry

Abstract

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.

8 pages, 1 figure; v2: clarifications in Sec.V, accepted for publication in Physical Review D

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Cited by in corpus (4)

• Line of Fixed Points in Gross-Neveu Theories
• Scale symmetry breaking and generation of mass at quantum critical points
• Fermion Mass Generation without Symmetry Breaking
• Mean-field theory for self-interacting relativistic Luttinger fermions