Renormalization-Group Evolution and Nonperturbative Behavior of Chiral Gauge Theories with Fermions in Higher-Dimensional Representations

Abstract

We study the ultraviolet to infrared evolution and nonperturbative behavior of a simple set of asymptotically free chiral gauge theories with an SU($N$) gauge group and an anomaly-free set of $n_{S_k}$ copies of chiral fermions transforming as the symmetric rank-$k$ tensor representation, $S_k$, and $n_{{\bar{A}}_{\ell }}$ copies of fermions transforming according to the conjugate antisymmetric rank-$\ell$ tensor representation, ${\bar{A}}_{\ell }$, of this group with $k,\ell \ge 2$. As part of our study, we prove a general theorem guaranteeing that a low-energy effective theory resulting from the dynamical breaking of an anomaly-free chiral gauge theory is also anomaly-free. We analyze the theories with $k=\ell =2$ in detail and show that there are only a finite number of these. Depending on the specific theory, the ultraviolet to infrared evolution may lead to a non-Abelian Coulomb phase, or may involve confinement with massless composite fermions, or fermion condensation with dynamical gauge and global symmetry breaking. We show that $S_k{\bar{A}}_k$ chiral gauge theories with $k\ge 3$ are not asymptotically free. We also analyze theories with fermions in $S_k$ and ${\bar{A}}_{\ell }$ representations of SU($N$) with $k\ne \ell$ and $k,\ell \ge 2$.

20 pages latex

References in corpus (4)

• Renormalization-Group Flows and Fixed Points in Yukawa Theories
• Patterns of Dynamical Gauge Symmetry Breaking
• Renormalization-Group Evolution of Chiral Gauge Theories
• Determination of SU(4)${}_{TC}$ Technicolor Gauge Group from Embedding in Extended Technicolor

Cited by in corpus (18)

• Spectroscopy of SU(4) composite Higgs theory with two distinct fermion representations
• Quantum Critical Behaviour of Semi-Simple Gauge Theories
• Patterns of Symmetry Breaking in Chiral "QCD"
• Probing the dynamics of chiral SU(N) gauge theories via generalized anomalies
• Scheme-Independent Calculations of Anomalous Dimensions of Baryon Operators in Conformal Field Theories
• On Swift Gravitons
• Dynamics and symmetries in chiral $SU(N)$ gauge theories
• Strong anomaly and phases of chiral gauge theories
• Anomalies and phases of strongly-coupled chiral gauge theories: recent developments
• Dynamical Abelianization and anomalies in chiral gauge theories
• If the Weak Were Strong and the Strong Were Weak
• Conformal Phase Diagram of Complete Asymptotically Free Theories
• ${\beta }_{IR}^{\prime }$ at an Infrared Fixed Point in Chiral Gauge Theories
• The global $B-L$ symmetry in the flavor-unified $\mathrm{SU}(N)$ theories
• The Standard Model quark/lepton masses and the Cabibbo-Kobayashi-Maskawa mixing in an $\mathrm{SU}(8)$ theory
• Dynamical Symmetry Breaking in Chiral Gauge Theories with Direct-Product Gauge Groups
• Confinement and XSB in QCD: Mysteries and beauty of soliton dynamics in nonAbelian gauge theories
• Ultraviolet to Infrared Evolution and Nonperturbative Behavior of $\mathrm{SU}(N)\otimes \mathrm{SU}(N-4)\otimes \mathrm{U}(1)$ Chiral Gauge Theories