Conformal Phase Transition in Gauge Theories

TL;DR

Conformal Phase Transition provides a framework for non-perturbative gauge dynamics by describing a continuous transition with an essential singularity in the order-parameter scaling, e.g., $X = \Lambda f(z)$, where $f(z)$ may behave as $f(z)\sim \exp(-1/(b\alpha^{(0)}))$ near criticality. It shows an abrupt reorganization of the light spectrum across the critical point, tied to conformal symmetry breaking via the partially conserved dilatation current (PCDC). The paper analyzes CPT realizations in the $D=2$ Gross-Neveu model, quenched QED4, and a pseudo-CPT in QED3, and discusses the structure of the low-energy effective action and phase diagrams in $SU(N_c)$ gauge theories, with implications for QCD and dynamical electroweak symmetry breaking. It emphasizes the role of marginal versus relevant operators in breaking conformal symmetry and the possible emergence of a dilaton-like state in low-energy dynamics.

Abstract

The conception of the conformal phase transiton (CPT), which is relevant for the description of non-perturbative dynamics in gauge theories, is introduced and elaborated. The main features of such a phase transition are established. In particular, it is shown that in the CPT there is an abrupt change of the spectrum of light excitations at the critical point, though the phase transition is continuous. The structure of the effective action describing the CPT is elaborated and its connection with the dynamics of the partially conserved dilatation current is pointed out. The applications of these results to QCD, models of dynamical electroweak symmetry breaking, and to the description of the phase diagram in (3+1)-dimensional $ SU(N_c)$ gauge theories are considered.