Critical Fermions with Spontaneously Broken Scale Symmetry

TL;DR

This paper investigates three-dimensional relativistic fermions with multi-fermion interactions, revealing a line of ultraviolet fixed points and spontaneous mass generation through broken scale invariance, with implications for conformal and higher spin theories.

Contribution

It uncovers a line of UV fixed points in fermionic theories and demonstrates spontaneous mass generation via broken scale symmetry, highlighting the role of parity violation.

Findings

Existence of a line of UV fixed points in fermionic theories

Spontaneous mass generation through broken scale invariance

Violation of hyperscaling relations in critical exponents

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.